Next Article in Journal
Learning Two-View Correspondences and Geometry via Local Neighborhood Correlation
Previous Article in Journal
Dynamic Time Warping Algorithm in Modeling Systemic Risk in the European Insurance Sector
Font Type:
Arial Georgia Verdana
Font Size:
Aa Aa Aa
Line Spacing:
Column Width:

Principle of Least Effort and Sentence Length in Public Speaking

Natalia L. Tsizhmovska
1 and
Leonid M. Martyushev
Technical Physics Department, Ural Federal University, 19 Mira St., 620002 Ekaterinburg, Russia
Institute of Industrial Ecology, Russian Academy of Sciences, 20 S. Kovalevskaya St., 620219 Ekaterinburg, Russia
Author to whom correspondence should be addressed.
Entropy 2021, 23(8), 1023;
Submission received: 19 July 2021 / Revised: 28 July 2021 / Accepted: 5 August 2021 / Published: 8 August 2021
(This article belongs to the Section Multidisciplinary Applications)


The analysis of sentence lengths in the inaugural speeches of US presidents and the annual speeches of UK party leaders is carried out. Transcripts of the speeches are used, rather than the oral production. It is discovered that the average sentence length in these speeches decreases linearly with time, with the slope of 0.13 ± 0.03 words/year. It is shown that among the analyzed distributions (log-normal, folded and half normal, Weibull, generalized Pareto, Rayleigh) the Weibull is the best distribution for describing sentence length. These two results can be considered a consequence of the principle of least effort. The connection of this principle with the well-known principles of maximum and minimum entropy production is discussed.

1. Introduction

The study of natural languages is extremely important not only for the human and social sciences, but also for the sciences that study the development patterns of complex systems (synergetics, cybernetics, etc.). An important section of language science is quantitative linguistics, which uses mathematical methods to establish language laws (note that the objectives and methods of quantitative linguistics go beyond the mere study of linguistic laws, see, e.g., [1,2]). At present, several similar laws are considered, and among them, the most famous are Zipf’s law, Herdan’s law, Brevity law, and Menzerath–Altmann’s law [3,4,5,6,7]. Such laws, found mostly by statistical methods, indicate existing regularities between various elements of language (phonemes, words, etc.).
The most important element of language is the sentence—the object of this study. According to the Cambridge dictionary, a sentence is a group of words, usually containing a verb, that expresses a thought in the form of a statement, question, instruction, or exclamation. Sentences have semantic completeness; they express a particular thought of a person and serve to communicate it with other people. Based on the above sentence qualities, the study of these structural units is essential for cognitive science, which is of great interest. A metaphor from atomic physics would be very appropriate to illustrate this, especially for representatives of the natural sciences. Many properties of an atom are estimated by radiation (spontaneous and stimulated) that an atom emits and/or absorbs. A person (human brain) also “emits” and perceives elementary flows of thought in the form of sentences and the characteristics of this “human radiation” can reveal a lot about both the person and their environment.
An important quantitative characteristic of a sentence is its length, which can be measured in various ways (the number of letters, words, etc.). The study of sentence lengths does not require special linguistic training and can be easily processed by computer. As a result, this value has been studied for a long time and is used to determine the authorship of a work, the genre of the text, the cognitive development of the author or reader (listener), the level of language proficiency, etc. [8,9,10,11,12,13,14]. Two regularities are noticed regarding sentence length.
The first regularity is a decrease in the average sentence length over time. The decrease may vary depending on the genre and language of the text [15,16,17,18]. In particular, according to analysis of English texts [15]: “fiction sentences are approximately (on average) 6.5 words shorter now than they were in the beginning of the nineteenth century”. The second regularity is the asymmetry of sentence length distribution in the text (their distribution functions are not normal). Various laws are proposed to describe sentence length distribution; log-normal is the most often, but it is also suggested to use others, in particular, gamma and hyperpascal distributions [4,6,19,20,21,22,23,24]. These regularities are associated with various factors; in particular, attempts are made to connect the log-normal distribution law with some stochastic multiplicative processes of sentence formation and the central limit theorem in logarithmic space [22]. There is no single general explanation of the noted regularities to date.
At the same time, the so-called principle of least effort [25] has existed for a long time in cognitive linguistics. According to this principle, language changes because speakers simplify their speech in various ways. This principle was suggested by G. Zipf. In 1949 he wrote: “a person, in solving his immediate problems, will view these against the background of his future problems, as estimated by himself. Moreover, he will strive to solve his problems in such a way as to minimize the total work that he must expend in solving both his immediate problems and his probable future problems. That in turn means that the person will strive to minimize the probable average rate of his work-expenditure (over time). And in so doing he will be minimizing his effort. Least effort, therefore, is a variant of least work.” [25]. Note that G. Zipf is not the first to consider this kind of principle. In discussing the close connection between thinking and language, it is necessary to mention E. Mach and his principle of the economy of thought (1864): “when the human mind, with its limited powers, attempts to mirror in itself the rich life of the world, of which it itself is only a small part, and which it can never hope to exhaust, it has every reason for proceeding economically” [26].
Starting with G. Zipf, the discussed principle of least effort is used to explain the different frequencies of words of various lengths, the origins of scaling in human language, etc. (see, e.g., [27,28]). However, even at the sentence level, this principle from a single position allows us to explain the two above-mentioned regularities. In fact, languages have evolved so that language users can communicate using sentences that are relatively easy to produce and comprehend. It is worth quoting a fragment from Ref. [29] “Various models of human sentence production and comprehension predict that long dependencies are difficult or inefficient to process; minimizing dependency length thus enables effective communication without incurring processing difficulty”. Thus, with a long-term observation of the language, sentence length will decrease. Let us consider the application of this principle for a significantly smaller timescale—creation time of the text by the author. The author strives to express each of his thoughts in the most economical, shortest way. As a result, the author consciously and unconsciously tends to use sentences of the minimum length (L), among the variety of those that are similar in content {L1, L2, …, Ln}, i.e., L = min{L1, L2, …, Ln}. It is well known from mathematical statistics [30,31] that the distribution of the minima of a random variable corresponds to the Weibull distribution (strictly, if L = min{L1, L2, …, Ln}, n→∞ and, L1, L2, …, Ln being identically distributed random variables equal to zero or larger, L will obey the Weibull distribution function [30,31]). Thus, the principle of least effort unambiguously indicates that sentence lengths, with a sufficiently large sample, should be described by the Weibull distribution, and not by any other distributions. It is interesting to note that the Weibull distribution is a two-parameter asymmetric distribution that generalizes the well-known one-parameter Rayleigh distribution and can be reduced to a gamma distribution by changing the variable.
The purpose of this work is to check the applicability of the Weibull distribution to the distribution of sentence lengths and to discover the law of the sentences length decrease over time. The results can provide additional justification for the applicability of the principle of least effort to elementary units of human speech that carry a particular thought.

2. Data for Analysis

The object of this research was to study the public speeches of politicians. Previously, this has beencarried out several times (see, e.g., [32,33,34]). However, the objectives of those studies were different from the objective of this work (readability and sentiment analysis, letter frequency distribution, etc.). Political speeches are a convenient object of research, since this is a form of oral speech that is well-documented for sufficiently long times. Political speeches are positioned between spoken and written ways of expressing thoughts. Unlike spoken speech, the speech under consideration is more meaningful, prepared ahead of time, and less spontaneous, from the speaker’s point of view. At the same time, in comparison with written speech, political speeches are more focused on the listener, and, therefore, have a greater emotional component and the tendency to be easily understood. As a result, political speeches are extremely valuable research material. Such speeches are usually focused on some “average” citizen—the voter—therefore, the processing of such data reflects the temporal changes in the majority of native speakers.
We analyzed text transcripts of the 59 inaugural speeches of US presidents from 1789 to 2021 and 224 texts of speeches of UK Party leaders from 1895 to 2018 (available in [35] and [36], respectively). The studied speeches of US presidents are uniformly distributed every four years. The time distribution of speeches of UK Party leaders was not so uniform (due to copyright, the appearance of a new large party in parliament in 1977, etc.), but much more extensive. Note that no UK speeches were processed for 1898, 1914–1917, 1931, 1938–1940, 1944, 1952–1954, or1959. The list of analyzed speeches is presented in Appendixes.
Sentence length was calculated from period to period, the unit of measurement was the words between spaces (prior to analysis, we replace all question marks, exclamation marks, and ellipses with a period, and also remove all dots used when writing decimal numbers). Note that the selected unit of measure for sentence length is not exclusive. Words were selected as a unit of measure for sentence length primarily because of the simplicity and the great prevalence of this approach. It is necessary to note that according to [37], sentence length is robust with respect to the selection of the unit of measurement. Thus, the choice of the word (and, e.g., not letters) will not lead to a change in the results of further analysis. The calculation was carried out automatically using a developed and tested computer program (see, example in Figure 1).
Despite the fact that the studied speeches belonged to a long period of time, the total number of words in the speeches did not change reliably (Figure 2). The average length of speech in words was 2331 ± 355 for the US and 5434 ± 774 for the UK.
Statistical analysis was performed using the well-known and widespread professional commercial product Statistica 12.0 (TIBCO Software). The data (year of the speech and values corresponding to the processed sentence lengths of speeches) are in open access [38].

3. Change in Sentence Length over Time

The parameters characterizing sentence length were calculated. They are listed below.
  • The average sentence length. To calculate this parameter, the total number of words in a speech was divided by the number of sentences. The change in this parameter over time is shown in Figure 3. The figure demonstrates that the average sentence length decreases linearly, with the slopes for USA and UK practically coinciding, and are equal to 0.13 ± 0.03 and 0.14 ± 0.01, respectively. On average, over 100 years, from 1900 to 2000, the average sentence length for both sets decreases from 30 to 16 words in a sentence, that is, the length is reduced by almost twice.
The median is known to be a stable characteristic of the distribution, it is almost unaffected by outliers. According to Figure 4, the median sentence length distribution decreases linearly in both sets with time. The slopes of the lines for USA and UK are 0.11 ± 0.02 and 0.11 ± 0.01, respectively. It can be seen that the lines are very close and practically coincide with ones for average sentence lengths.
The decrease in sentence length over time is also demonstrated in Figure 5, where the time dependence of the maximum sentence length is presented. The decrease in this parameter in both sets is approximately linear.
The final results of this section are summarized in Table 1.

4. Analysis of the Sentence Length Distribution Law

To analyze the sentence length distribution law, a number of speeches of the US presidents were excluded from the initial data. First, small speech texts, containing less than 40 sentences were excluded (these are speech texts of 1789, 1793, 1797, 1813, 1829, 1833, 1849, 1865, 1869, 1905, and 1945). Second, since it is the texts of public oral speeches that are analyzed, the texts of 1953, 1961, 1973, and 1981 were excluded because these speeches were not spoken, but were only written. Third, speech texts of 1801, 1805, 1837, 1877, 1881, 1893, 1941, 1965, and 1969 were not processed, since these speech texts have a multimodal distribution (the reasons for this and the analysis of these distributions could be the subject of a separate work). Thus, the analysis of the distribution law was carried out at 31 inaugural speeches of US presidents. All 224 speeches of the UK party leaders were analyzed. However, 31 texts were excluded due to the low significance level (<0.05) of the results obtained in relation to all tested distribution laws. Single outliers were excluded from the datasets before data analysis.
Six distributions with no more than two parameters, such as log-normal, Weibull, folded normal, half normal (normal), generalized Pareto, Rayleigh were analyzed in order to find the best theoretical distribution that describes the studied empirical distributions. The ranking of these distributions by the quality of data description was carried out according to the Kolmogorov–Smirnov criterion: the larger the p-level value, the better this distribution describes the empirical data and, accordingly, the higher its place in comparison with others. Table 2 and Table 3 show the number of times one of the six listed sentence length distributions was among the top three (see Appendix A for more information).
Table 2 shows that, in 14 inaugural speeches of the US presidents, the Weibull distribution took first place in terms of significance, in another 14 it took second place, and in 3, it took third place. Thus, the Weibull distribution is the only distribution that adequately describes all speeches and takes the top three places. The average distribution significance level, where Weibull was in the first place, is 0.73, and for the second and third places, it is 0.5 and 0.3, respectively (see Appendix A). The log-normal distribution, ranked in the top three for 19 speeches, describes the data somewhat worse than Weibull one. The average significance levels for the log-normal distribution are 0.67 for the first place (13 speeches), 0.37 for the second place (5 speeches) and 0.08 for the third place (1 speech). Similar results can be seen for UK speeches (see Table 3 and Appendix A).
Thus, according to the performed statistical analysis, the Weibull distribution is the most preferable for describing the studied speeches. The Weibull distribution (cumulative distribution function) has the form 1 − exp(− (x/λ)k), where λ and k are the scale and shape parameters respectively. Examples of the experimental data description using the Weibull distribution are presented in Figure 6. Note that the one-parameter Rayleigh distribution, ranked third in the description quality according to the analysis results, is a special case of the Weibull distribution, where the shape parameter is equal to two (see Table 2 and Table 3).
The behavior of the parameters of the Weibull distribution over time is shown in Figure 7 and Figure 8 (see Appendix B for numerical details). It follows from the Figure 7 that the scale parameter reliably decreases over time. Since this parameter is known to be directly proportional to the mean, median, and mode of the Weibull distribution, this once again confirms the above statement about the decrease in the average (and the most probable) sentence length. The shape parameter for US speeches does not reliably change over time and is equal to 1.9 ± 0.1. At the same time, the shape parameter for UK speeches is slightly increasing, changing from 1.5 to 1.8 over the past 100 years. This is the only difference found when comparing sentence lengths for US and UK speeches. Since the change over time is not large (the slope of the line is 0.002 ± 0.001), for reliability, an analysis of this result using additional data is required. Table 4 summarizes the results on the behavior of the parameters of the Weibull distribution over time.
Thus, the time behavior of the parameters of the Weibull distribution allows us to conclude that, over the past two hundred years, sentence length distribution has become less fuzzy, the width of the peak decreases, and its abscissa is slightly shifted to the left. This is demonstrated in Figure 9. As a result, over time, speeches become composed of similar in length and shorter sentences, the difference in length decreases. In terms of sentence lengths, the text becomes more ordered. This can be seen in Figure 10, where information entropy (Shannon entropy) is presented as a function of time. The calculation of this value was based on sentence length distribution histograms containing the probabilities of detecting sentence length in a speech at a certain length interval.

5. Conclusions

Based on the calculation of sentence lengths in the text transcripts of the inaugural speeches of the US presidents for 228 years and the annual speeches of the UK party leaders for 123 years, two main results were obtained:
1. The average sentence length for both US and UK speeches decreases linearly with time with the slope of 0.13 ± 0.03 words/year and, on average, from 1900 to 2000, sentence length decreased with time from 30 to 16 words.
2. Sentence length distribution for both US and UK speeches is better described by the Weibull distribution (in particular, in comparison with the log-normal). The scale parameter of this distribution reliably decreases over time from 35 to 15. The shape parameter for US speeches does not change over time and is equal to 1.9 ± 0.1, and the shape parameter for UК speeches slightly changes over time from 1.5 to 1.8.
These two results are in agreement with the principle of least effort: the speaker, attempting to minimize both their efforts and the listeners’ effort, tends to choose the shortest possible sentence length from a potential set of sentences of approximately the same content. As a result, on the one hand, sentence length distribution begins to correspond to the distribution of minimum values—the Weibull distribution, and on the other hand, at time intervals significantly longer than the speech preparation time, the average sentence length decreases. The detected change over time in the scale parameter of the Weibull distribution and in information entropy indicates that sentence length in public speeches is gradually becoming less diverse; it is being unified and standardized.
Here we highlight the following idea. When establishing the distribution type for empirical data, most important are not statistical tests, but rather the theoretical justification. If we accept the principle of least effort, then the Weibull distribution clearly follows from it. If one assumes that the principle of least effort is not suitable here, then obviously, they must propose some other theoretical justification—their principle—and theoretically derive, for example, gamma or lognormal distributions from it. Currently, we do not see such attempts. The G. Zipf’s principle, in our opinion, is very profound and productive, and many interesting consequences can be obtained from it. It has great potential, which has not yet been fully embraced by modern linguists. Our work and a number of works (see, e.g., [27,28,39,40,41,42,43]) show how useful it can be.
An interesting continuation of this work can be the verification of the obtained results using breath groups [6]. Detecting correlations and differences in such a collaborative analysis of breath groups (largely related to human physiology) and sentence lengths (largely related to cognitive processes) is a very interesting task. One of the problems in this direction will be a significantly smaller statistical database for breath groups in comparison with an almost limitless database for sentence lengths. Another interesting development of this work, in the scope of currently well-established directions connected to language complex networks (see, e.g., [39,40,41,42,43]), could be an analysis of the data obtained, here, from the position of the principle of compression, which appeared as a development of the ideas of G. Zipf [43]. It seems to us that the results of this work, combined with the principle of compression and with the use of Kolmogorov complexity ideas (existing inalgorithmic information theory) could be very promising. Found patterns for English also require validation for other languages, including artificial, as well as using other methods and linguistic units (letters, initial characters, words, etc.). In this regard, works [44,45,46] may be useful.
In conclusion, we return to the metaphor from physics given in the introduction. The analysis of the atom emission spectra and the Planck formula for wavelength distribution revolutionized the understanding of atomic properties, leading to the formulation of the laws of the quantum world—quantum mechanics. The distribution law of the lengths of utterances (sentences) “emitted” by the brain, corresponding to the Weibull distribution, is also able to stimulate the development of brain sciences. One of the possible directions related to brain biophysics may be the study of the energetic basis of the origin and development of thought and language. There are a number of works in this direction, in particular [4,6,47,48,49,50,51,52,53]. Considering thought as a complex non-equilibrium process, it can be concluded that its development matches the well-known principle of maximum entropy production. According to this principle, causes (stimuli) generate such responses that maximize the thermodynamic entropy production [47,54,55]. One of these responses in the course of the evolution of human thinking was the origin of the language. This revolutionary bifurcation process led to an abrupt increase in energy consumption and, as a result, an increase in the entropy production in a nonequilibrium system, i.e., in neural networks of humans who have become users of language. Naturally, a spontaneously emerged structure (network) could not be optimal at inception: only a certain basic structure (framework) of language was formed, which had some imperfections. Subsequently, being already at the high level of energy consumption and entropy production achieved after bifurcation, the nonequilibrium system began to evolve for a rather long time, trying to minimize energy consumption [54,55]. This minimization will no longer return the system to its previous, pre-bifurcation values of entropy production; however, due to the optimization of the neural network processes responsible for language, a small decrease is possible. According to nonequilibrium thermodynamics, this optimization process is already progressing in accordance with the Prigogine minimum production principle [47,54,55]. Its linguistic analogue can be considered the principle of least effort (least effort assumes less energy spent on communication, and, consequently, less energy dissipation). The information on the “simplification” of language—a decrease in its entropy, discovered in this work, can be considered a confirmation that language is currently going through a second (minimizing) stage of development.

Author Contributions

L.M.M.: Conceptualization, Methodology, Supervision, Investigation, Writing—original draft, Writing—review and editing. N.L.T.: Investigation, Software, Validation, Computation, Visualization, Reading—review and editing. All authors have read and agreed to the published version of the manuscript.


This research received no external funding.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

Not applicable.

Conflicts of Interest

The authors declare no conflict of interest.

Appendix A

Ranking the suitability of theoretical distribution laws for the observed empirical sentence length distributions based on the Kolmogorov–Smirnov criterion. After the name of the distribution, its p-level is given:
YearI Place, p-ValueII Place, p-ValueIII Place, P-Value
1817Weibull, 0.80Log Normal, 0.52Rayleigh, 0.33
1821Log Normal, 0.51Weibull, 0.41Rayleigh, 0.20
1825Log Normal, 0.97Weibull, 0.79Folded Normal, 0.56
1841Log Normal, 0.98Weibull, 0.38Rayleigh, 0.10
1845Log Normal, 0.72Weibull, 0.30Rayleigh, 0.02
1857Folded Normal, 0.97Weibull, 0.96Normal, 0.90
1861Weibull, 0.91Log Normal, 0.45Normal, 0.16
1873Rayleigh, 0.86Weibull, 0.85Folded Normal, 0.62
1885Weibull, 0.80Folded Normal, 0.66Normal, 0.59
1889Rayleigh, 0.54Weibull, 0.54Folded Normal, 0.24
1897Weibull, 0.57Log Normal, 0.52Rayleigh, 0.49
1909Weibull, 0.97Rayleigh, 0.72Folded Normal, 0.68
1913Log Normal, 0.54Weibull, 0.18Half Normal, 0.12
1917Log Normal, 0.85Weibull, 0.30Half Normal, 0.12
1921Weibull, 0.43Log Normal, 0.18Rayleigh, 0.06
1925Rayleigh, 0.25Weibull, 0.20Log Normal, 0.08
1929Weibull, 0.26Rayleigh, 0.13Folded Normal, 0.03
1941Log Normal, 0.75Weibull, 0.73Folded Normal, 0.17
1949Log Normal, 0.54Weibull, 0.54Folded Normal, 0.19
1957Log Normal, 0.56Rayleigh, 0.26Weibull, 0.24
1977Weibull, 0.90Rayleigh, 0.75Normal, 0.65
1985Log Normal, 0.40Weibull, 0.22Rayleigh, 0.09
1989Log Normal, 0.72Rayleigh, 0.5Weibull, 0.49
1993Weibull, 0.89Folded Normal, 0.59Rayleigh, 0.54
1997Log Normal, 0.41Rayleigh, 0.20Weibull, 0.18
2001Weibull, 0.45Log Normal, 0.19Folded Normal, 0.18
2005Weibull, 0.92Folded Normal, 0.56Normal, 0.53
2009Weibull, 0.97Half Normal, 0.23General Pareto, 0.16
2013Log Normal, 0.75Weibull, 0.63Rayleigh, 0.60
2017Weibull, 0.71Folded Normal, 0.51Normal, 0.33
2021Weibull, 0.67Log Normal, 0.31Folded Normal, 0.01
Year, PartyI Place, p-ValueII Place, p-ValueIII Place, p-Value
1895 LiberalLog Normal, 0.37Weibull, 0.37Folded Normal, 0.01
1896 LiberalLog Normal, 0.46Weibull, 0.28Normal, 0.00
1897 LiberalLog Normal, 0.06Weibull, 0.01Half Normal, 0.00
1897 ConservativeWeibull, 0.47Log Normal, 0.22Half Normal, 0.02
1899 LiberalWeibull, 0.29Log Normal, 0.15Normal, 0.00
1900 ConservativeWeibull, 0.87Folded Normal, 0.64Log Normal, 0.57
1901 LiberalWeibull, 0.31Log Normal, 0.07Half Normal, 0.05
1902 ConservativeFolded Normal, 0.46Half Normal, 0.46Weibull, 0.30
1903 ConservativeWeibull, 0.84Half Normal, 0.39Log Normal, 0.26
1903 LiberalWeibull, 0.51Folded Normal, 0.08Normal, 0.06
1904 ConservativeWeibull, 0.64Folded Normal, 0.42General Pareto, 0.18
1905 LiberalWeibull, 0.18Log Normal, 0.14Half Normal, 0.01
1906 ConservativeHalf Normal, 0.37Weibull, 0.36General Pareto, 0.23
1907 ConservativeGeneral Pareto, 0.25Weibull, 0.16Log Normal, 0.13
1907 LiberalWeibull, 0.53Half Normal, 0.13Normal, 0.09
1908 LiberalWeibull, 0.59Folded Normal, 0.13Half Normal, 0.13
1908 ConservativeWeibull, 0.66Log Normal, 0.45Half Normal, 0.27
1909 LiberalWeibull, 0.69Folded Normal, 0.3Log Normal, 0.05
1909 ConservativeWeibull, 0.34Log Normal, 0.34Half Normal, 0.16
1910 LiberalWeibull, 0.38Folded Normal, 0.27Half Normal, 0.26
1910 ConservativeWeibull, 0.92Half Normal, 0.24Folded Normal, 0.24
1911 ConservativeWeibull, 0.72Log Normal, 0.13Folded Normal, 0.07
1912 LiberalWeibull, 0.55Log Normal, 0.3Folded Normal, 0.21
1912 ConservativeWeibull, 0.17Log Normal, 0.14Half Normal, 0.03
1913 ConservativeLog Normal, 0.11Weibull, 0.07Half Normal, 0.02
1913 LiberalWeibull, 0.91Log Normal, 0.28Folded Normal, 0.26
1918 LiberalWeibull, 0.82Rayleigh, 0.17Log Normal, 0.07
1919 LiberalWeibull, 0.98Half Normal, 0.12Log Normal, 0.09
1920 LiberalWeibull, 0.66Folded Normal, 0.65Half Normal, 0.62
1920 ConservativeWeibull, 0.02Log Normal, 0.02Folded Normal, 0.01
1921 LiberalWeibull, 0.67Log Normal, 0.63Half Normal, 0.23
1921 ConservativeLog Normal, 0.58Weibull, 0.09Half Normal, 0.07
1922 LiberalWeibull, 0.90Half Normal, 0.73General Pareto, 0.51
1922 ConservativeWeibull, 0.52Log Normal, 0.48Folded Normal, 0.10
1923 LiberalWeibull, 0.85General Pareto, 0.25Normal, 0.15
1924 LiberalLog Normal, 0.85Weibull, 0.50Folded Normal, 0.26
1924 LabourWeibull, 0.77Half Normal, 0.24Folded Normal, 0.24
1924 ConservativeWeibull, 0.75Log Normal, 0.39Folded Normal, 0.11
1925 LiberalLog Normal, 0.83Weibull, 0.60Rayleigh, 0.33
1925 ConservativeWeibull, 0.47Log Normal, 0.02Normal, 0.02
1926 ConservativeWeibull, 0.21Log Normal, 0.09Rayleigh, 0.01
1927 LiberalLog Normal, 0.67Weibull, 0.21Folded Normal, 0.01
1927 ConservativeLog Normal, 0.47Weibull, 0.19Folded Normal, 0.01
1928 LiberalLog Normal, 0.35Weibull, 0.04Half Normal, 0.00
1928 ConservativeLog Normal, 0.45Weibull, 0.01Folded Normal, 0.00
1929 LiberalLog Normal, 0.37Weibull, 0.19Folded Normal, 0.03
1929 ConservativeLog Normal, 0.67Weibull, 0.61Folded Normal, 0.05
1930 LiberalWeibull, 0.16Log Normal, 0.00Normal, 0.00
1932 ConservativeWeibull, 0.78Log Normal, 0.23Normal, 0.10
1932 LiberalLog Normal, 0.52Weibull, 0.45Folded Normal, 0.03
1933 ConservativeLog Normal, 0.70Weibull, 0.57Folded Normal, 0.08
1934 ConservativeWeibull, 0.75Folded Normal, 0.72Normal, 0.67
1935 ConservativeWeibull, 0.61Folded Normal, 0.53Rayleigh, 0.32
1936 LiberalLog Normal, 0.89Weibull, 0.19Folded Normal, 0.03
1937 LiberalWeibull, 0.74Folded Normal, 0.46Log Normal, 0.41
1941 LiberalWeibull, 0.68Log Normal, 0.54Rayleigh, 0.43
1942 LiberalWeibull, 0.67Rayleigh, 0.38Log Normal, 0.31
1943 LiberalLog Normal, 0.74Weibull, 0.51Normal, 0.07
1945 LiberalWeibull, 0.62Rayleigh, 0.23Normal, 0.11
1946 LabourLog Normal, 0.29Weibull, 0.08Normal, 0.00
1947 LabourLog Normal, 0.76Weibull, 0.21Normal, 0.01
1948 LabourLog Normal, 0.85Weibull, 0.51Normal, 0.04
1949 LabourWeibull, 0.47Log Normal, 0.38Folded Normal, 0.08
1950 LabourLog Normal, 0.55Weibull, 0.39Normal, 0.11
1951 LabourLog Normal, 0.85Weibull, 0.19Rayleigh, 0.02
1955 ConservativeWeibull, 0.32Log Normal, 0.29Rayleigh, 0.03
1956 ConservativeWeibull, 0.11Log Normal, 0.07Folded Normal, 0.01
1957 ConservativeLog Normal, 0.38Weibull, 0.05Folded Normal, 0.00
1958 ConservativeLog Normal, 0.15Weibull, 0.13Rayleigh, 0.09
1960 ConservativeWeibull, 0.53Rayleigh, 0.35Folded Normal, 0.03
1961 ConservativeWeibull, 0.68Rayleigh, 0.1Log Normal, 0.04
1962 ConservativeWeibull, 0.49Rayleigh, 0.17Log Normal, 0.17
1963 LiberalLog Normal, 0.58Weibull, 0.09Rayleigh, 0.01
1963 ConservativeLog Normal, 0.52Rayleigh, 0.43Weibull, 0.32
1964 LabourWeibull, 0.75Folded Normal, 0.18Log Normal, 0.08
1965 LabourLog Normal, 0.1Weibull, 0.09General Pareto, 0.02
1965 ConservativeLog Normal, 0.49Weibull, 0.25Normal, 0.00
1966 LabourWeibull, 0.46Folded Normal, 0.06Log Normal, 0.02
1966 ConservativeWeibull, 0.32Log Normal, 0.19Folded Normal, 0.02
1967 LabourWeibull, 0.66Folded Normal, 0.04Log Normal, 0.01
1967 ConservativeLog Normal, 0.36Weibull, 0.13Half Normal, 0.00
1968 LabourWeibull, 0.73Folded Normal, 0.07Log Normal, 0.01
1968 ConservativeLog Normal, 0.22Weibull, 0.16Rayleigh, 0.00
1969 LabourWeibull, 0.55Folded Normal, 0.03Normal, 0.00
1969 ConservativeWeibull, 0.18Log Normal, 0.05Half Normal, 0.00
1970 LabourWeibull, 0.28Log Normal, 0.03Folded Normal, 0.01
1970 ConservativeLog Normal, 0.41Weibull, 0.35Rayleigh, 0.16
1971 ConservativeLog Normal, 0.21Weibull, 0.15Rayleigh, 0.1
1971 LabourWeibull, 0.43Folded Normal, 0.05Normal, 0.01
1972 ConservativeLog Normal, 0.37Weibull, 0.21Folded Normal, 0.07
1972 LabourWeibull, 0.66Log Normal, 0.06Normal, 0.00
1973 ConservativeLog Normal, 0.17Weibull, 0.01Folded Normal, 0.00
1973 LabourWeibull, 0.57Folded Normal, 0.1Normal, 0.04
1974 LabourWeibull, 0.81Log Normal, 0.02Normal, 0.01
1975 ConservativeLog Normal, 0.53Weibull, 0.28Rayleigh, 0.06
1975 LabourWeibull, 0.41Folded Normal, 0.04Log Normal, 0.02
1976 ConservativeWeibull, 0.23Log Normal, 0.07Normal, 0.00
1976 LabourWeibull, 0.24Log Normal, 0.05Normal, 0.00
1977 ConservativeWeibull, 0.48Normal, 0.03Rayleigh, 0.03
1997 LabourWeibull, 0.54Log Normal, 0.03Folded Normal, 0.01
1977 Liberal aWeibull, 0.66Log Normal, 0.10Rayleigh, 0.02
1977l Liberal bLog Normal, 0.67Weibull, 0.3Folded Normal, 0.01
1978 ConservativeWeibull, 0.26Log Normal, 0.04Folded Normal, 0.01
1978 LabourWeibull, 0.19Log Normal, 0.01Normal, 0.00
1978 LiberalWeibull, 0.28Log Normal, 0.12Folded Normal, 0.05
1979 ConservativeLog Normal, 0.30Weibull, 0.12Folded Normal, 0.00
1979 LabourWeibull, 0.17Log Normal, 0.02Folded Normal, 0.00
1989 LiberalWeibull, 0.58Rayleigh, 0.03Normal, 0.02
1980 ConservativeWeibull, 0.45Rayleigh, 0.37Log Normal, 0.17
1980 LabourLog Normal, 0.14Weibull, 0.02Folded Normal, 0.00
1980 LiberalWeibull, 0.63Log Normal, 0.11Rayleigh, 0.02
1981 ConservativeWeibull, 0.69Rayleigh, 0.08Log Normal, 0.08
1981 LabourLog Normal, 0.51Weibull, 0.20Half Normal, 0.00
1981 LiberalWeibull, 0.31Log Normal, 0.19Folded Normal, 0.02
1982 SDP-Liberal Alliance bWeibull, 0.69Folded Normal, 0.34Rayleigh, 0.34
1982 ConservativeWeibull, 0.18Rayleigh, 0.05Log Normal, 0.05
1982 LabourWeibull, 0.96Rayleigh, 0.26Normal, 0.15
1982 LiberalWeibull, 0.24Log Normal, 0.05Rayleigh, 0.01
1983 ConservativeWeibull, 0.17Log Normal, 0.13Rayleigh, 0.06
1983 LabourWeibull, 0.57Folded Normal, 0.1Rayleigh, 0.08
1983 LiberalWeibull, 0.51Rayleigh, 0.41Folded Normal, 0.05
1984 ConservativeWeibull, 0.81Folded Normal, 0.21Normal, 0.02
1984 LabourWeibull, 0.60Normal, 0.05Folded Normal, 0.04
1984 LiberalWeibull, 0.07Rayleigh, 0.02Log Normal, 0.00
1985 ConservativeWeibull, 0.23Log Normal, 0.10Rayleigh, 0.05
1985 LabourLog Normal, 0.42Weibull, 0.29Half Normal, 0.08
1985 LiberalWeibull, 0.63Log Normal, 0.08Rayleigh, 0.05
1986 ConservativeWeibull, 0.35Log Normal, 0.09Folded Normal, 0.07
1986 LabourWeibull, 0.64Log Normal, 0.04Normal, 0.01
1986 LiberalWeibull, 0.28Log Normal, 0.01Folded Normal, 0.01
1987 ConservativeWeibull, 0.51Rayleigh, 0.09Log Normal, 0.02
1987 LabourWeibull, 0.21Log Normal, 0.06Folded Normal, 0.01
1987 SDP-Liberal Alliance aWeibull, 0.61Log Normal, 0.25Folded Normal, 0.15
1987 SDP-Liberal Alliance bLog Normal, 0.37Weibull, 0.16Rayleigh, 0.03
1988 ConservativeWeibull, 0.47Rayleigh, 0.09Folded Normal, 0.03
1988 LabourLog Normal, 0.22Weibull, 0.03Half Normal, 0.00
1988 LiberalLog Normal, 0.9Weibull, 0.42Rayleigh, 0.07
1989 ConservativeWeibull, 0.12Rayleigh, 0.05Log Normal, 0.01
1989 LabourLog Normal, 0.09Weibull, 0.06Half Normal, 0.00
1990 ConservativeWeibull, 0.16Log Normal, 0.02Folded Normal, 0.00
1990 LabourLog Normal, 0.24Weibull, 0.02Half Normal, 0.00
1991 ConservativeWeibull, 0.11Log Normal, 0.01Rayleigh, 0.00
1991 LabourWeibull, 0.11Log Normal, 0.04Normal, 0.00
1992 ConservativeWeibull, 0.26Folded Normal, 0.00Log Normal, 0.00
1992 LabourWeibull, 0.42Log Normal, 0.05Rayleigh, 0.00
1992 Liberal Democrat lWeibull, 0.39Log Normal, 0.18Normal, 0.00
1993 ConservativeWeibull, 0.23Log Normal, 0.02Folded Normal, 0.00
1993 LabourWeibull, 0.51Rayleigh, 0.22Normal, 0.09
1993 Liberal DemocratFolded Normal, 0.51Weibull, 0.43Normal, 0.10
1994 ConservativeWeibull, 0.11Log Normal, 0.05Normal, 0.00
1994 LabourWeibull, 0.36Log Normal, 0.01Normal, 0.00
1994 Liberal DemocratWeibull, 0.88Folded Normal, 0.17Rayleigh, 0.14
1995 ConservativeWeibull, 0.17Rayleigh, 0.01Log Normal, 0.00
1995 LabourLog Normal, 0.25Weibull, 0.12Half Normal, 0.00
1996 ConservativeLog Normal, 0.14Weibull, 0.03Folded Normal, 0.00
1996 LabourLog Normal, 0.26Weibull, 0.03Folded Normal, 0.00
1996 Liberal DemocratWeibull, 0.44Log Normal, 0.003Normal, 0.00
1997 ConservativeWeibull, 0.44Folded Normal, 0.33Log Normal, 0.31
1997 LabourLog Normal, 0.12Weibull, 0.001Half Normal, 0.00
1998 ConservativeWeibull, 0.07Log Normal, 0.05Folded Normal, 0.00
1998 LabourLog Normal, 0.19Weibull, 0.13Folded Normal, 0.00
1988 Liberal DemocratWeibull, 0.09Log Normal, 0.001Folded Normal, 0.00
1999 ConservativeLog Normal, 0.07Weibull, 0.04Folded Normal, 0.00
1999 LabourLog Normal, 0.01Half Normal, 0.00Weibull, 0.00
1999 Liberal Democrat aWeibull, 0.74Folded Normal, 0.28Log Normal, 0.15
1999 Liberal Democrat bLog Normal, 0.04Weibull, 0.00Rayleigh, 0.00
2000 ConservativeWeibull, 0.01Log Normal, 0.01Normal, 0.00
2000 LabourLog Normal, 0.02Weibull, 0.00Folded Normal, 0.00
2000 LLog Normal, 0.01Weibull, 0.00Half Normal, 0.00
2001 ConservativeLog Normal, 0.17Weibull, 0.1Folded Normal, 0.02
2001 LabourLog Normal, 0.52Weibull, 0.00Half Normal, 0.00
2001 Liberal DemocratWeibull, 0.13Log Normal, 0.06Half Normal, 0.00
2002 ConservativeWeibull, 0.28Rayleigh, 0.27Log Normal, 0.14
2002 LabourLog Normal, 0.10Weibull, 0.00Folded Normal, 0.00
2002 Liberal DemocratWeibull, 0.21Rayleigh, 0.05Folded Normal, 0.03
2003 ConservativeWeibull, 0.16Rayleigh, 0.11Folded Normal, 0.01
2003 LabourLog Normal, 0.20Weibull, 0.02Half Normal, 0.00
2003 Liberal DemocratWeibull, 0.05Rayleigh, 0.03Folded Normal, 0.00
2004 ConservativeWeibull, 0.08Rayleigh, 0.07Folded Normal, 0.00
2004 LabourWeibull, 0.24Log Normal, 0.18Half Normal, 0.01
2004 Liberal Democrat lWeibull, 0.19Folded Normal, 0.01Log Normal, 0.00
2005 ConservativeWeibull, 0.64Rayleigh, 0.30Log Normal, 0.14
2005 LabourWeibull, 0.07Log Normal, 0.05Folded Normal, 0.00
2005 Liberal DemocratRayleigh, 0.20Weibull, 0.19Log Normal, 0.11
2006 Conservative aWeibull, 0.15Log Normal, 0.05Folded Normal, 0.00
2006 Conservative bWeibull, 0.01Log Normal, 0.00Rayleigh, 0.00
2006 LabourLog Normal, 0.12Weibull, 0.03Folded Normal, 0.00
2006 Liberal DemocratLog Normal, 0.24Weibull, 0.03Rayleigh, 0.01
2007 ConservativeWeibull, 0.10Log Normal, 0.09Folded Normal, 0.00
2007 LabourWeibull, 0.16Rayleigh, 0.02Log Normal, 0.02
2007 Liberal DemocratRayleigh, 0.19Weibull, 0.11Log Normal, 0.05
2008 ConservativeWeibull, 0.17Log Normal, 0.03Normal, 0.00
2008 LabourWeibull, 0.19Log Normal, 0.06Rayleigh, 0.01
2008 Liberal Democrat lWeibull, 0.49Rayleigh, 0.07Normal, 0.01
2009 ConservativeWeibull, 0.06Log Normal, 0.01Rayleigh, 0.00
2009 LabourRayleigh, 0.68Weibull, 0.53Folded Normal, 0.1
2009 Liberal DemocratWeibull, 0.17Rayleigh, 0.05Folded Normal, 0.01
2010 ConservativeWeibull, 0.23Log Normal, 0.00Folded Normal, 0.00
2010 LabourWeibull, 0.45Folded Normal, 0.04Rayleigh, 0.02
2010 Liberal Democrat lLog Normal, 0.16Weibull, 0.03Rayleigh, 0.01
2011 ConservativeWeibull, 0.30Rayleigh, 0.0003Log Normal, 0.00
2011 LabourLog Normal, 0.02Weibull, 0.01Normal, 0.00
2011 Liberal DemocratWeibull, 0.25Folded Normal, 0.00Log Normal, 0.00
2012 ConservativeWeibull, 0.16Folded Normal, 0.02Half Normal, 0.01
2012 LabourWeibull, 0.01Log Normal, 0.01Folded Normal, 0.00
2012 Liberal DemocratWeibull, 0.49Log Normal, 0.13Rayleigh, 0.03
2013 ConservativeWeibull, 0.19Log Normal, 0.03Folded Normal, 0.00
2013 LabourLog Normal, 0.11Weibull, 0.02Normal, 0.00
2013 Liberal DemocratWeibull, 0.64Rayleigh, 0.11Normal, 0.03
2014 Conservative Weibull, 0.13Log Normal, 0Folded Normal, 0.00
2014 LabourWeibull, 0.17Folded Normal, 0.01Rayleigh, 0.00
2014 Liberal DemocratWeibull, 0.32Folded Normal, 0.13Normal, 0.03
2015 Conservative Weibull, 0.2Folded Normal, 0.001Log Normal, 0.00
2015 LabourWeibull, 0.18Log Normal, 0.01Rayleigh, 0.00
2015 Liberal DemocratWeibull, 0.42Folded Normal, 0.07Rayleigh, 0.03
2016 Conservative Log Normal, 0.23Weibull, 0.01Normal, 0.00
2016 LabourWeibull, 0.37Rayleigh, 0.31Log Normal, 0.12
2016 Liberal DemocratLog Normal, 0.14Weibull, 0.07Normal, 0.00
2017 ConservativeLog Normal, 0.05Weibull, 0.02Normal, 0.00
2017 LabourWeibull, 0.16Log Normal, 0.1Folded Normal, 0.01
2017 Liberal DemocratWeibull, 0.31Rayleigh, 0.11Folded Normal, 0.04
2018 ConservativeLog Normal, 0.12Rayleigh, 0.01Weibull, 0.003
2018 LabourRayleigh, 0.18Weibull, 0.16Log Normal, 0.09
2018 Liberal DemocratWeibull, 0.41Rayleigh, 0.1Log Normal, 0.09

Appendix B

The shape and scale parameters for the Weibull distributions used for the description of the empirical sentence length distributions
Yearp-Value λ , Scalek, Shape
Year, Partyp-Value λ , Scalek, Shape
1895 Liberal0.3733.71.6
1896 Liberal0.2828.31.6
1897 Conservative0.4732.61.5
1899 Liberal0.2932.91.6
1900 Conservative0.8738.21.7
1901 Liberal0.3125.31.4
1902 Conservative0.3035.01.3
1903 Conservative0.8436.41.3
1903 Liberal0.5129.51.5
1904 Conservative0.6440.21.5
1905 Liberal0.1829.31.5
1906 Conservative0.3636.21.4
1907 Conservative0.1634.61.2
1907 Liberal0.5335.91.5
1908 Liberal0.5932.51.4
1908 Conservative0.6638.01.3
1909 Liberal0.6938.71.6
1909 Conservative0.3432.41.4
1910 Liberal0.3831.51.4
1910 Conservative0.9231.11.4
1911 Conservative0.7226.91.5
1912 Liberal0.5536.01.4
1912 Conservative0.1725.41.4
1913 Conservative0.0727.01.4
1913 Liberal0.9138.71.5
1918 Liberal0.8233.61.8
1919 Liberal0.9833.21.5
1920 Liberal0.6630.01.4
1921 Liberal0.6727.11.4
1921 Conservative0.0924.21.3
1922 Liberal0.9028.41.4
1922 Conservative0.5228.31.5
1923 Liberal0.8533.41.6
1924 Liberal0.5032.41.9
1924 Labour0.7728.41.4
1924 Conservative0.7533.81.6
1925 Liberal0.6030.41.9
1925 Conservative0.4732.01.6
1926 Conservative0.2133.71.7
1927 Liberal0.2123.31.6
1927 Conservative0.1925.91.6
1929 Liberal0.1920.31.7
1929 Conservative0.6126.91.5
1930 Liberal0.1622.01.7
1932 Conservative0.7825.21.8
1932 Liberal0.4529.71.6
1933 Conservative0.5730.31.7
1934 Conservative0.7530.11.8
1935 Conservative0.6134.21.8
1936 Liberal0.1935.21.4
1937 Liberal0.7438.62.4
1941 Liberal0.6830.81.8
1942 Liberal0.6727.01.8
1943 Liberal0.5136.01.7
1945 Liberal0.6227.11.7
1946 Labour0.0821.31.7
1947 Labour0.2119.61.6
1948 Labour0.5124.41.7
1949 Labour0.4723.51.8
1950 Labour0.3923.01.8
1951 Labour0.1921.31.8
1955 Conservative0.3223.71.7
1956 Conservative0.1119.71.8
1958 Conservative0.1321.71.9
1960 Conservative0.5320.12
1961 Conservative0.6821.11.8
1962 Conservative0.4923.11.9
1963 Liberal0.0922.61.8
1963 Conservative0.3227.52.0
1964 Labour0.7534.61.7
1965 Labour0.0929.61.3
1965 Conservative0.2519.91.6
1966 Labour0.4630.91.6
1966 Conservative0.3225.81.6
1967 Labour0.6627.01.5
1967 Conservative0.1324.01.5
1968 Labour0.7322.41.6
1968 Conservative0.1620.31.7
1969 Labour0.5517.81.7
1969 Conservative0.1821.31.5
1970 Labour0.2825.01.5
1970 Conservative0.3525.61.9
1971 Conservative0.1524.12.0
1971 Labour0.4326.11.6
1972 Conservative0.2124.11.9
1972 Labour0.6624.31.6
1973 Labour0.5725.31.6
1974 Labour0.8129.11.7
1975 Conservative0.2824.61.8
1975 Labour0.4126.21.5
1976 Conservative0.2316.61.6
1976 Labour0.2422.81.7
1977 Conservative0.4819.51.7
1997 Labour0.5424.41.6
1977 Liberal a0.6626.31.7
1977l Liberal b0.326.11.7
1978 Conservative0.2618.41.7
1978 Labour0.1921.81.6
1978 Liberal0.2822.41.8
1979 Conservative0.1217.61.7
1979 Labour0.1727.11.5
1989 Liberal0.5821.21.8
1980 Conservative0.4520.22.0
1980 Liberal0.6323.81.7
1981 Conservative0.6921.61.8
1981 Labour0.226.71.7
1981 Liberal0.3123.51.8
1982 SDP-Liberal Alliance b0.6925.91.9
1982 Conservative0.1817.61.9
1982 Labour0.9631.31.8
1982 Liberal0.2420.41.7
1983 Conservative0.1719.11.8
1983 Labour0.5729.51.8
1983 Liberal0.5122.42.0
1984 Conservative0.8119.51.7
1984 Labour0.623.81.6
1984 Liberal0.0721.21.8
1985 Conservative0.2316.71.8
1985 Labour0.2927.71.4
1985 Liberal0.6320.11.8
1986 Conservative0.3518.31.8
1986 Labour0.6427.91.6
1986 Liberal0.2821.21.7
1987 Conservative0.5117.11.9
1987 Labour0.2125.51.6
1987 SDP-Liberal Alliance a0.6118.21.7
1987 SDP-Liberal Alliance b0.1620.51.9
1988 Conservative0.4716.51.9
1988 Liberal0.4220.61.8
1989 Conservative0.1216.91.9
1989 Labour0.0622.01.5
1990 Conservative0.1615.11.7
1991 Conservative0.1113.01.8
1991 Labour0.1122.71.6
1992 Conservative0.2612.81.7
1992 Labour0.4223.81.7
1992 Liberal Democrat0.3918.81.6
1993 Conservative0.2317.51.6
1993 Labour0.5125.61.8
1993 Liberal Democrat0.4319.91.7
1994 Conservative0.1119.61.6
1994 Labour0.3619.61.6
1994 Liberal Democrat0.8817.81.8
1995 Conservative0.1712.71.8
1995 Labour0.1221.71.5
1996 Liberal Democrat0.4415.31.6
1997 Conservative0.4417.11.6
1998 Conservative0.0718.11.7
1998 Labour0.1320.91.6
1988 Liberal Democrat0.0913.11.5
1999 Liberal Democrat a0.7415.91.7
2001 Conservative0.118.02.4
2001 Liberal Democrat0.1313.41.5
2002 Conservative0.2816.82.0
2002 Liberal Democrat0.2113.41.9
2003 Conservative0.1611.41.9
2003 Liberal Democrat0.0512.41.9
2004 Conservative0.0812.02.0
2004 Labour0.2417.71.2
2004 Liberal Democrat0.1914.81.6
2005 Conservative0.6416.71.9
2005 Labour0.0716.41.6
2005 Liberal Democrat0.1915.32.0
2006 Conservative a0.1513.01.6
2007 Conservative0.123.21.7
2007 Labour0.1623.81.9
2007 Liberal Democrat0.1114.72.0
2008 Conservative0.1716.21.6
2008 Labour0.1925.61.8
2008 Liberal Democrat0.4912.31.9
2009 Conservative0.0615.11.8
2009 Labour0.5323.82.0
2009 Liberal Democrat0.1713.41.9
2010 Conservative0.2314.51.6
2010 Labour0.4518.31.8
2011 Conservative0.314.51.7
2011 Liberal Democrat0.2511.91.6
2012 Conservative0.1615.21.4
2012 Liberal Democrat0.4919.41.8
2013 Conservative0.1914.41.6
2013 Liberal Democrat0.6420.81.8
2014 Conservative0.1316.71.6
2014 Labour0.1714.91.8
2014 Liberal Democrat0.3220.51.7
2015 Conservative0.215.51.6
2015 Labour0.1815.71.7
2015 Liberal Democrat0.4218.11.8
2016 Labour0.3723.62.0
2016 Liberal Democrat0.0716.81.5
2017 Labour0.1619.71.8
2017 Liberal Democrat0.3117.21.8
2018 Labour0.1621.52.0
2018 Liberal Democrat0.4118.71.8


  1. Köhler, R.; Altmann, G. Aims and methods of quantitative linguistics. In Problems of Quantitative Linguistic; RAM-Verlag: Ludenscheid, Germany, 2005; pp. 12–42. [Google Scholar]
  2. Köhler, R. Synergetic linguistics. In Contributions to quantitative linguistics; Köhler, R., Rieger, B.B., Eds.; Springer: Berlin, Germany, 1991; pp. 41–51. [Google Scholar]
  3. Best, K.H.; Rottmann, O. Quantitative Linguistics, an Invitation; RAM-Verlag: Ludenscheid, Germany, 2017. [Google Scholar]
  4. Hernández-Fernández, A.; Torre, I.G.; Garrido, J.-M.; Lacasa, L. Linguistic Laws in Speech: The Case of Catalan and Spanish. Entropy 2019, 21, 1153. [Google Scholar] [CrossRef] [Green Version]
  5. Corral, Á.; Serra, I. The brevity law as a scaling law, and a possible origin of zipf’s law for word frequencies. Entropy 2020, 22, 224. [Google Scholar] [CrossRef] [PubMed] [Green Version]
  6. Torre, I.G.; Luque, B.; Lacasa, L.; Kello, C.T.; Hernández-Fernández, A. On the physical origin of linguistic laws and lognormality in speech. R. Soc. Open Sci. 2019, 6, 191023. [Google Scholar] [CrossRef] [Green Version]
  7. Liu, H.T.; Xu, C.S.; Liang, J. Dependency distance: A new perspective on syntactic patterns innatural languages. Phys. Life Reviews 2017, 21, 171–193. [Google Scholar] [CrossRef] [PubMed]
  8. Udny Yule, G. In sentence- length as a statistical characteristic of style in prose: With application to two cases of disputed authorship. Biometrika 1939, 30, 363–390. [Google Scholar]
  9. Lesskis, G.A. O zavisimosti mezhdu razmerom predlozheniya i kharakterom teksta. J. Vopr. Jazykoznaniya. 1963, 3, 92–112. (In Russian) [Google Scholar]
  10. Admoni, V.G. Razmer predlozheniya i slovosochetaniya kak yavleniye sintaksicheskogo stroya. J. Vopr. Jazykoznaniya. 1966, 4, 111–118. (In Russian) [Google Scholar]
  11. Burdayeva, T.V. Variantnost’ Slozhnopodchinennogo Predlozheniya i Ekvivalentnykh yemu Struktur. Ph.D. Thesis, Samara State Pedagogical University, Samara, Russia, 26 June 2002. (In Russian). [Google Scholar]
  12. Kamshilova, O.N.; Kapotova, N.S.; Razumova, V.V. Issledovaniye dliny i struktury predlozheniya v spetsial’nom korpuse tekstov. Korpusnaya Lingvistika; St. Petersburg University Publ: Saint Petersburg, Russia, 2008; pp. 183–187. (In Russian) [Google Scholar]
  13. Kučera, H. Computational analysis of predicational structures in English. In Proceedings of the Coling: The 8th International Conference on Computational Linguistics, Tokyo, Japan, 30 September–4 October 1980; Volume 1, pp. 32–38. [Google Scholar]
  14. Kornai, A. How many words are there? Glottometrics 2002, 4, 61–86. [Google Scholar]
  15. Rudnicka, K. Variation of Sentence Length Across Time and Genre: Influence on the Syntactic Usage in English. Stud. Corpus Linguist. 2018, 85, 219–240. [Google Scholar]
  16. Grigoryeva, Y.U.M. Dlina predlozheniya kak pokazatel’ sintaksicheskikh izmeneniy v yazyke (na materiale perevodov Biblii na shvedskiy yazyk 1917 i 2000 gg.). Skandinavskaya Filologiya 2012, 12, 16–24. (In Russian) [Google Scholar]
  17. Drutman, L. Is Congress Getting Dumber, or Just More Plainspoken? Available online: 2012 (accessed on 25 July 2021).
  18. Ostermeier, E. My Message is Simple: Obama’s SOTU Written at 8th Grade Level for Third Straight Year. Available online: 2012 (accessed on 25 July 2021).
  19. Sobkowicz, P.; Thelwall, M.; Buckley, K.; Georgios Paltoglou, G.; Sobkowicz, A. Lognormal distributions of user post lengths in Internet discussions—a consequence of the Weber-Fechner law? EPJ Data Sci. 2013, 2, 2. [Google Scholar] [CrossRef] [Green Version]
  20. Ishida, M.; Ishida, K. On distributions of sentence lengths in Japanese writing. Glottometrics. 2007, 15, 28–44. [Google Scholar]
  21. Sigurd, B.; Eeg-Olofsson, M.; Van de Weijer, J. Word length, sentence length and frequency—Zipf revisited. Studia Linguistica 2004, 58, 37–52. [Google Scholar] [CrossRef]
  22. Furuhashi, S.; Hayakawa, Y. Lognormality of the distribution of Japanese sentence lengths. J. Phys. Soc. Jpn. 2012, 81, 034004. [Google Scholar] [CrossRef]
  23. Williams, C.B. A note on the statistical analysis of sentence-length as a criterion of literary style. Biometrika 1940, 31, 356–361. [Google Scholar] [CrossRef]
  24. Wake, W.C. Sentence-length distributions of Greek authors. J. R. Stat. Soc. Ser. A 1957, 120, 331–346. [Google Scholar] [CrossRef]
  25. Zipf, G.K. Human Behavior and the Principle of Least Effort: An Introduction to Human Ecology; Addison-Wesley Publishing: Cambridge, UK, 1949. [Google Scholar]
  26. Mach, E. Popular Scientific Lectures; The Open Court Publishing Company: Chicago, IL, USA, 1894. [Google Scholar]
  27. Ferrer i Cancho, R.; Solé, R.V. Least effort and the origins of scaling in human language. Proc. Natl. Acad. Sci. USA 2003, 100, 788–791. [Google Scholar] [CrossRef] [Green Version]
  28. Ferrer i Cancho, R. Non-crossing dependencies: Least effort, not grammar. In Towards a Theoretical Framework for Analyzing Complex Linguistic Networks; Mehler, A., Ed.; Springer: Berlin/Heidelberg, Germany, 2016; pp. 203–234. [Google Scholar]
  29. Futrell, R.; Mahowald, K.; Gibson, E. Large-scale evidence of dependency length minimization in 37 languages. Proc. Natl. Acad. Sci. USA 2015, 112, 10336–10341. [Google Scholar] [CrossRef] [Green Version]
  30. Gumbel, E. Statistics of Extremes; Columbia University Press: New York, NY, USA, 1962. [Google Scholar]
  31. Leadbetter, M.R.; Rootzen, H.; Lindgren, G. Extremes and Related Properties of Random Sequences and Processes; Springer: New York, NY, USA, 1983. [Google Scholar]
  32. Tucker, E.C.; Capps, C.J.; Shamir, L. A data science approach to 138 years of congressional speeches. Heliyon 2020, 6, e04417. [Google Scholar] [CrossRef] [PubMed]
  33. Božić Lenard, D. Gender differences in the length of words and sentences on the corpus of congressional speeches. Imp. J. Interdiscip. Res. 2016, 2, 1417–1424. [Google Scholar]
  34. Li, W.; Miramontes, P. Fitting ranked english and spanish letter frequency distribution in US and Mexican presidential speeches. J. Quant. Linguist. 2011, 18, 359–380. [Google Scholar] [CrossRef]
  35. Inaugural Addresses of the Presidents of the United States. Available online: (accessed on 25 July 2021).
  36. British Political Speech, Swansea University, UK. Available online: (accessed on 25 July 2021).
  37. Vieira, D.S.; Picoli, S.; Mendes, R.S. Robustness of sentence length measures in written texts. Phys. A Stat. Mech. Appl. 2018, 506, 749–754. [Google Scholar] [CrossRef] [Green Version]
  38. Tsizhmovska, N.L. Sentence Length in Public Speaking, Ural Federal University, Russia, 2021. Available online: (accessed on 25 July 2021).
  39. Baronchelli, A.; Ferrer-i-Cancho, R.; Pastor-Satorras, R.; Chater, N.; Christiansen, M.H. Networks in cognitive science. Trends Cogn. Sci. 2013, 17, 348–360. [Google Scholar] [CrossRef] [PubMed] [Green Version]
  40. Ferrer i Cancho, R.; Solé, R.V.; Köhler, R. Patterns in syntactic dependency networks. Phys. Rev. E. 2004, 69, 051915. [Google Scholar] [CrossRef] [PubMed] [Green Version]
  41. Solé, R.V.; Ferrer-Cancho, R.; Montoya, J.M.; Valverde, S. Selection, tinkering, and emergence in complex networks. Complexity 2002, 8, 20–33. [Google Scholar] [CrossRef]
  42. Solé, R.V.; Corominas-Murtra, B.; Valverde, S.; Steels, L. Language networks: Their structure, function, and evolution. Complexity 2010, 15, 20–26. [Google Scholar] [CrossRef]
  43. Ferrer i Cancho, R.; Hernández-Fernández, A.; Lusseau, D.; Agoramoorthy, G.; Hsu, M.J.; Semple, S. Compression as a universal principle of animal behavior. Cogn. Sci. 2013, 37, 1565–1578. [Google Scholar] [CrossRef] [PubMed] [Green Version]
  44. Shulzinger, E.; Bormashenko, E. On the Universal Quantitative Pattern of the Distribution of Initial Characters in General Dictionaries: The Exponential Distribution is Valid for Various Languages. J. Quant. Linguist. 2017, 24, 273–288. [Google Scholar] [CrossRef]
  45. Shulzinger, E.; Legchenkova, I.; Bormashenko, E. Co-occurrence of the Benford-like and Zipf Laws Arising from the Texts Representing Human and Artificial Languages. arXiv 2018, arXiv:1803.03667. [Google Scholar]
  46. Drożdż, S.; Oświȩcimka, P.; Kulig, A.; Kwapień, J.; Bazarnik, K.; Grabska-Gradzińska, I.; Rybicki, J.; Stanuszek, M. Quantifying origin and character of long-range correlations in narrative texts. Inf. Sci. 2016, 331, 32–44. [Google Scholar] [CrossRef] [Green Version]
  47. Kirkaldy, J.S. Thermodynamics of the human brain. Biophys. J. 1965, 5, 981–986. [Google Scholar] [CrossRef] [Green Version]
  48. Swenson, R.; Turvey, M.T. Thermodynamics reasons for perception-action cycle. Ecol. Psychol. 1991, 4, 317–348. [Google Scholar] [CrossRef]
  49. Kondepudi, D. Self-organization, entropy production, and physical intelligence. Ecol. Psychol. 2021, 24, 33–45. [Google Scholar] [CrossRef]
  50. Barrett, N. On the nature and origins of cognition as a form of motivated activity. Adapt. Behavior. 2020, 28, 89–103. [Google Scholar] [CrossRef]
  51. Guevara Erra, R.; Mateos, D.M.; Wennberg, R.; Perez Velazquez, J.L. Statistical mechanics of consciousness: Maximization of information content of network is associated with conscious awareness. Phys. Rev. E. 2016, 94, 052402–052411. [Google Scholar] [CrossRef] [Green Version]
  52. Mateos, D.M.; Guevara Erra, R.; Wennberg, R.; Perez Velazquez, J.L. Measures of entropy and complexity in altered states of consciousness. Cogn Neurodyn. 2018, 12, 73–84. [Google Scholar] [CrossRef] [PubMed]
  53. Perez Velazquez, J.L.; Mateos, D.M.; Guevara Erra, R. On a simple general principle of brain organization. Front. Neurosci. 2019, 13, 1106. [Google Scholar] [CrossRef] [PubMed] [Green Version]
  54. Martyushev, L.M.; Seleznev, V.D. Maximum entropy production principle in physics, chemistry and biology. Phys. Rep. 2006, 426, 1–45. [Google Scholar] [CrossRef]
  55. Martyushev, L.M. Entropy and entropy production: Old misconceptions and new breakthroughs. Entropy 2013, 15, 1152–1170. [Google Scholar] [CrossRef] [Green Version]
Figure 1. Example of sentence length calculation by the algorithm used in the study.
Figure 1. Example of sentence length calculation by the algorithm used in the study.
Entropy 23 01023 g001
Figure 2. Number of words in the text N versus time t. Red circles indicate data for USA, and black triangles indicate data for UK.
Figure 2. Number of words in the text N versus time t. Red circles indicate data for USA, and black triangles indicate data for UK.
Entropy 23 01023 g002
Figure 3. Average sentence length A as a function of the time speaking t. Red circles indicate data for USA, and black triangles indicate data for UK. The linear regression equation for USA is 286–0.13t and for UK is 299–0.14t.
Figure 3. Average sentence length A as a function of the time speaking t. Red circles indicate data for USA, and black triangles indicate data for UK. The linear regression equation for USA is 286–0.13t and for UK is 299–0.14t.
Entropy 23 01023 g003
Figure 4. Median M as a function of the time speaking t. Red circles indicate data for USA, and black triangles indicate data for UK. The linear regression equation for USA is 232–0.11t and for UK is 240–0.11t.
Figure 4. Median M as a function of the time speaking t. Red circles indicate data for USA, and black triangles indicate data for UK. The linear regression equation for USA is 232–0.11t and for UK is 240–0.11t.
Entropy 23 01023 g004
Figure 5. Maximum sentence length Max, as a function of the time speaking t. Red circles indicate data for USA, and black triangles indicate data for UK. The linear regression equation for USA is 1317–0.6t with the slope of 0.6 ± 0.3. The linear regression equation for UK is 1197–0.6t with the slope of 0.6 ± 0.1.
Figure 5. Maximum sentence length Max, as a function of the time speaking t. Red circles indicate data for USA, and black triangles indicate data for UK. The linear regression equation for USA is 1317–0.6t with the slope of 0.6 ± 0.3. The linear regression equation for UK is 1197–0.6t with the slope of 0.6 ± 0.1.
Entropy 23 01023 g005
Figure 6. Sentence length distribution histogram. (a) USA speech, 1817; 119 points. The solid line is the Weibull distribution, for which р-level is 0.80, λ = 28.4 and k = 1.8; (b) UK Labour Party, 1992; 256 points. The dashed line is the Weibull distribution, for which р-level is 0.42, λ = 23.8 and k = 1.7.
Figure 6. Sentence length distribution histogram. (a) USA speech, 1817; 119 points. The solid line is the Weibull distribution, for which р-level is 0.80, λ = 28.4 and k = 1.8; (b) UK Labour Party, 1992; 256 points. The dashed line is the Weibull distribution, for which р-level is 0.42, λ = 23.8 and k = 1.7.
Entropy 23 01023 g006
Figure 7. Behavior of the scale parameter λ of the Weibull distribution versus the time t. Red circles indicate data for USA, and black triangles indicate data for UK. The linear regression equation for USA is 209.8–0.09t with the slope of 0.09 ± 0.03. The linear regression equation for UK is 321.5–0.15t with the slope of 0.15 ± 0.02.
Figure 7. Behavior of the scale parameter λ of the Weibull distribution versus the time t. Red circles indicate data for USA, and black triangles indicate data for UK. The linear regression equation for USA is 209.8–0.09t with the slope of 0.09 ± 0.03. The linear regression equation for UK is 321.5–0.15t with the slope of 0.15 ± 0.02.
Entropy 23 01023 g007
Figure 8. Behavior of the shape parameter k of the Weibull distribution versus the time t for UK. The linear regression equation is -2.9 + 0.002t (the slope of the line is 0.002 ± 0.001).
Figure 8. Behavior of the shape parameter k of the Weibull distribution versus the time t for UK. The linear regression equation is -2.9 + 0.002t (the slope of the line is 0.002 ± 0.001).
Entropy 23 01023 g008
Figure 9. Weibull distribution histograms showing the change in sentence length distributions over time. (a) Data for USA, the shape parameter is 1.9, the scale parameters are 40.2, 29.2 and 18.2 for 1789, 1905 and 2021, respectively. (b) Data for UK, the shape parameters are 1.4, 1.6, 1.7 and the scale parameters are 34.6, 25.2 and 15.9 for 1895, 1957 and 2018, respectively.
Figure 9. Weibull distribution histograms showing the change in sentence length distributions over time. (a) Data for USA, the shape parameter is 1.9, the scale parameters are 40.2, 29.2 and 18.2 for 1789, 1905 and 2021, respectively. (b) Data for UK, the shape parameters are 1.4, 1.6, 1.7 and the scale parameters are 34.6, 25.2 and 15.9 for 1895, 1957 and 2018, respectively.
Entropy 23 01023 g009
Figure 10. Information entropy S versus the time t. Red circles indicate data for USA, and black triangles indicate data for UK. The linear regression equation for USA is 7.7–0.003t (the slope of the line is 0.003 ± 0.001) and for UK is 8.2–0.003t (the slope of the line is 0.003 ± 0.001).
Figure 10. Information entropy S versus the time t. Red circles indicate data for USA, and black triangles indicate data for UK. The linear regression equation for USA is 7.7–0.003t (the slope of the line is 0.003 ± 0.001) and for UK is 8.2–0.003t (the slope of the line is 0.003 ± 0.001).
Entropy 23 01023 g010
Table 1. Time behavior of the average sentence length.
Table 1. Time behavior of the average sentence length.
Parameters Characterizing Sentence LengthLinear Fitting, Confidence Level, Coefficient of Determination
Average286 − (0.13 ± 0.03)t, 95%, 0.67299 – (0.14 ± 0.01)t, 95%, 0.64
Median232 – (0.11 ± 0.02)t, 95%, 0.64240 – (0.11 ± 0.01)t, 95%, 0.57
Maximum value1317 – (0.6 ± 0.3)t, 95%, 0.191197 – (0.6 ± 0.1)t, 95%, 0.29
Table 2. Ranking of distributions according to the Kolmogorov–Smirnov criterion. US speeches.
Table 2. Ranking of distributions according to the Kolmogorov–Smirnov criterion. US speeches.
WeibullLog-NormalRayleighFolded NormalNormalGeneral Pareto
Table 3. Ranking of distributions according to the Kolmogorov–Smirnov criterion. UK speeches.
Table 3. Ranking of distributions according to the Kolmogorov–Smirnov criterion. UK speeches.
WeibullLog-NormalRayleighFolded NormalNormalGeneral Pareto
Table 4. Parameters of the Weibull distribution for USA and UK speeches.
Table 4. Parameters of the Weibull distribution for USA and UK speeches.
Parameters of the Weibull DistributionLinear Fitting, Confidence Level, Coefficient of Determination
Scale (λ)209.8 − (0.09 ± 0.03)t, 95%, 0.63 321.5 − (0.15 ± 0.02)t, 95%, 0.64
Shape (k)1.9 ± 0.1, 95%−2.9 + (0.002 ± 0.001)t, 95%, 0.19
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Share and Cite

MDPI and ACS Style

Tsizhmovska, N.L.; Martyushev, L.M. Principle of Least Effort and Sentence Length in Public Speaking. Entropy 2021, 23, 1023.

AMA Style

Tsizhmovska NL, Martyushev LM. Principle of Least Effort and Sentence Length in Public Speaking. Entropy. 2021; 23(8):1023.

Chicago/Turabian Style

Tsizhmovska, Natalia L., and Leonid M. Martyushev. 2021. "Principle of Least Effort and Sentence Length in Public Speaking" Entropy 23, no. 8: 1023.

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

Article Metrics

Back to TopTop