Political Mobilization in the Laboratory: The Role of Norms and Communication
2. Related Literature
3.1. Experiment 1 (E1): The Partisan Case
3.2. Experiment 2 (E2): The Non-Partisan Case
4. Experimental Design
5. Treatments, Hypotheses and Procedures
6.1. Experiment 1: The Partisan Case
6.1.1. The Impact of Mobilization
6.1.2. The Impact of Normative Appeals
6.1.3. Content Analysis of the Normative Appeals
6.1.4. Regression Analysis
6.2. Experiment 2: The Non-Partisan Case
6.2.1. The Impact of Mobilization
6.2.2. The Impact of Normative Appeals
6.2.3. Content Analysis of the Normative Appeals
6.2.4. Regression Analysis
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Appendix A. Theoretical Framework—Experiment 1
Appendix A.1. Participation Probabilities for Beta Players
Appendix A.2. Quantal Response Equilibrium
Appendix A.2.1. Beta Players
Appendix A.2.2. Alpha Players
Appendix A.3. Implemented Parameterization and Equilibrium Predictions
Appendix B. Theoretical Framework—Experiment 2
Appendix B.1. Quantal Response Equilibrium
Appendix B.1.1. Beta Players
Appendix B.1.2. Alpha Players
Appendix B.2. Implemented Parameterization and Equilibrium Predictions
Appendix C. Experimental Instructions
- Task 1
- Task 2
- Alpha Member
- Beta Member
|Number of Discs Bought by the Group||Multiplied Discs|
- Budget, Activation Costs and Disc Buying Costs
Appendix D. Trust Game Results
Appendix E. Analysis of Normative Appeal Features
Appendix F. Transcript of Alphas’ Messages
Appendix F.1. Experiment 1
- Session A (5-5, 4-5):
- Session B (5-4, 1-1):
- Session C (5-5, 5-4):
- Session D(5-5, 4-5):
- Session E (5-4, 1-1):
- Session F (5-5, 5-4):
Appendix F.2. Experiment 2
- Session A (4)
- Session B (3, 5)
- Session C (3, 5)
- Session D (4, 5, 1)
- Session E (4, 5, 1)
- Session F (3, 5, 5)
- Session G (4, 5, 4)
- Session H (5, 3, 5)
- Session I (4, 5, 4)
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Rosenstone and Hansen  define mobilization as the “process by which candidates, parties, activists and groups induce other people to participate.” Most commonly studied have been the cases of get-out-the-vote drives and partisan appeals by campaigns, but examples also include “distributing voter registration forms and absentee ballots, driving people to the polls on election day, or providing child care to free parents to attend meetings and demonstrations”.
This framework builds on the pivotal voter framework described by Palfrey and Rosenthal , which relies on strong rationality assumptions. In Section 3.1, I briefly elaborate on some of the assumptions underlying the model and how they might apply to real-world elections. More generally, Feddersen  discusses how the literature has evolved from the original contribution of Palfrey and Rosenthal, which relies on extreme assumptions of rationality and information, to extensions that accommodate group mobilization and ethical voting agents.
The words of Cox  echo this limitation: “the main theoretical critique of elite mobilization models has been that they lack micro foundations. That is, they do not explain precisely what elites do and why their followers respond by bearing the costs of participation”.
Of course, in reality citizens should be able to activate themselves—i.e., register for voting or transport themselves to the polls. However, allowing for an intermediate phase where Betas who had not been activated could activate themselves would add another stage to the model and complicate the framework considerably. The gain would be marginal as the purpose of the model is to test the behavioral response of subjects who have been activated by an Alpha member and compare it to the response of those who have been activated by a computer.
This modeling assumption imposes a minimal degree of rationality on Alphas, as low Betas cost less to activate and participate at higher rates in equilibrium. In a real-world setting, Alphas must also be able to gauge Beta’s costs of voting in order to mobilize those that have lower costs of voting. There are several observable characteristics that campaigns have access to and that correlate with voting costs, either material (such as physical distance to the polls or ability to reach the polls through own transportation) or psychological (such as the amount of political information the voter has access to).
The model does not have a closed form solution for most group sizes (), as the probability terms in are non-linear. Numerical methods can be used to obtain Nash equilibria (NE) and related solution concepts, such as QRE. QRE has three main advantages over NE. First, a greater ability to explain experimental data, particularly from tests of political participation models . Second, QRE selects equilibria. Participation games typically have several NE, both in pure and mixed strategies. QRE selects the one that tends to have good empirical verification in the laboratory. Third, QRE retains most of the important features of NE—e.g., the probability of choosing a certain strategy is increasing in the payoff difference to the alternative(s) and beliefs are consistent in equilibrium. A more detailed discussion can be found in Appendix A.2.
In other words, there is only one cost type in E2, as no differences in behavior were found across cost types in E1, which will be discussed in the Results section.
The first of E2’s nine sessions had an exchange rate of 0.12, which was adjusted to 0.15 for the remaining sessions in order to equalize the earnings in E1 and E2.
A meta-study by Johnson and Mislin  shows that, on average, senders hand over of their endowment to receivers. Receivers send back of the multiplied amount, on average. This leads to an approximate equalization of payoffs. Appendix D provides a concise description of the trust game data.
75.7% and 81.6% of subjects employed mixed strategies in E1 and E2, respectively.
There were three available ratings: ‘satisfied’, ‘neutral’, and ‘dissatisfied’. An analysis of this data is available upon request.
In the proposed model, players’ preferences do not explicitly account for reciprocity for two main reasons. First, applying the model of Dufwenberg and Kirchsteiger  makes reciprocity exclusively dependent on beliefs about how kind other players are. As the authors note, a good set of predictions requires a proper measurement of first- and second-order beliefs, which is possible but would complicate the experimental design further. Second, in the case of both Dufwenberg and Kirchsteiger  and Falk et al. , the parameter that governs reciprocity preferences is exogenous and therefore would have to be estimated from data for the predictions not to be ad hoc. The calibration of the model would require more than a simple trust game. To be sure, the authors apply their models to games that are substantially simpler than the ones presented in this paper.
E1 further allows me to observe the behavioral response from high- and low-cost subjects. I conjecture that the former, who require a larger mobilization effort, will reciprocate mobilization to a greater extent and participate more. It is well known that campaigns and activists target those who are more likely to participate—i.e., those who have low participation costs ). Often, those with the lowest participation costs (the more educated, the more mobile, etc.) are also the cheapest to mobilize. To the best of my knowledge, there is no evidence on how citizens with different mobilization costs respond to the mobilization effort.
Two pilot sessions (48 subjects) were run prior to E1. These sessions implemented a different parameter configuration and served the purpose of testing subject comprehension of the experimental protocol and providing data for the model calibration. Those data are not part of this paper.
In fact, one could argue that an Alpha behaving according to the selfish preference model commands no reciprocity, as they would simply be maximizing earnings. The collected data would allow us to test that conjecture. At any rate, the experimenter must grant Alphas freedom in their decisions in order to create scope for reciprocity concerns.
The observed null effect of mobilization could in principle be due to a differential response from high and low cost subjects. Along the reciprocity rationale, low-cost subjects might not be responsive to activation while high-cost subjects might be. However, the response to treatments is not more pronounced for high-cost subjects (W-MP ).
It has been shown that within-group discussion in participation games leads to increased participation [40,41,42]. Open discussion allows subjects to propose, discuss and commit to a given strategy. It also allows subjects to infer others’ intentions. Important differences exist between these open discussion protocols and my experiments’ one-way appeals. The messages sent by the Alpha can propose a strategy and motivate it, but no commitment for the participation game is present, as Alphas cannot participate themselves. The absence of two-way interaction reduces the scope of promise exchange between Alphas and Betas. Even though Alphas could potentially convey intentions about future activation decisions (sub-blocks 5 and 6), that was never the case.
The participation decision was framed as “buying a disc” in the experiment. Subjects were told that the group in which most subjects bought a disc would win that round of the game, and so on. An appeal to buy a disc is therefore equivalent to an appeal for participation.
These numbers are based on content analysis carried out by four independent coders. The procedure is explained in the next sub-section.
Excluding those groups in Ctr where a message was not sent (two cases) and where the message was only one word (one case), the difference is still insignificant (WMW ).
The coders were not part of the same subject pool. They were given instructions such that they were able to understand the experiment but were not told about the research questions or treatments.
Excluding the groups where no message was sent does not alter this result (WMW ).
The other substantial difference between E1 and E2 is the absence of two cost types in the latter case.
To be sure, equilibrium mobilization depends on anticipated (equilibrium) participation by the Betas. In fact, over-mobilization by the Alphas might be an equilibrium response if they expect over-participation from the Betas.
The two most relevant ones are pure strategy NE and ‘totally quasi-symmetric Nash equilibria’, in which all players use mixed strategies and players in the same group employ the same strategy. Namely, for , there exists a unique NE where both players choose to participate. The same equilibrium exists for all cases where . When and , the game reduces to a public goods game. For such games, there exists pure strategy NE in which one player in i participates and the others abstain. For and , there also exists a mixed-strategy NE. For , several mixed-strategy NEs exist. These results are available upon request.
A maximum likelihood estimation using data from the pilot sessions yields for the low Betas and for high Betas. The reason for this is that, as we saw in Section 6.1, high Betas over-participate relative to any admissible prediction and therefore bias the estimate in the direction of random behavior.
|Group size||Activation cost: high|
|Number of low Betas||Activation cost: low|
|Benefit for the winning group||Participation cost: high|
|Benefit for the losing group||Participation cost: low|
|0||6.50, 6.50||5.11, 7.39||5.26, 6.74||5.26, 5.74||5.25, 4.75||5.25, 3.75|
|1||7.39, 5.11||6.00, 6.00||4.92, 6.58||4.94, 5.56||4.94, 4.56||4.93, 3.57|
|2||6.74, 5.26||6.58, 4.92||5.50, 5.50||4.81, 5.19||4.75, 4.25||4.69, 3.31|
|3||5.74, 5.26||5.56, 4.94||5.19, 4.81||4.50, 4.50||4.09, 3.91||3.94, 3.06|
|4||4.75, 5.25||4.56, 4.94||4.25, 4.75||3.91, 4.09||3.50, 3.50||3.22, 2.78|
|5||3.75, 5.25||3.57, 4.93||3.31, 4.69||3.06, 3.94||2.78, 3.22||2.50, 2.50|
|Group size||Marginal per capita return|
|Activation cost||Endowment/participation cost|
|Model 1||Model 2|
|Coeff.||Mg. Effect (%)||Coeff.||Mg. Effect (%)|
|Appeal||0.26 ***||1.43 ***||0.06||0.27|
|Activation*Appeal||0.40 ***||2.23 ***|
|Activation Level||0.57 ***||2.73 ***||0.57 ***||2.53 ***|
|Cost||−0.75 ***||−2.62 ***||−0.76 ***||−2.42 ***|
|Constant||−1.61 ***||−1.56 ***|
|Model 1||Model 2|
|Coeff.||Mg. Effect (%)||Coeff.||Mg. Effect (%)|
|Appeal||0.26 ***||1.66 ***||0.07||1.08|
|Activation*Appeal||0.32 ***||2.08 *|
|Trust||0.07 *||0.37 *||0.07 *||0.36 *|
|Reciprocity (High)||0.09||0.53||0.10 **||0.53 *|
|Activation Level||0.14 ***||0.79 ***||0.14 ***||0.78 ***|
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Robalo, P. Political Mobilization in the Laboratory: The Role of Norms and Communication. Games 2021, 12, 24. https://doi.org/10.3390/g12010024
Robalo P. Political Mobilization in the Laboratory: The Role of Norms and Communication. Games. 2021; 12(1):24. https://doi.org/10.3390/g12010024Chicago/Turabian Style
Robalo, Pedro. 2021. "Political Mobilization in the Laboratory: The Role of Norms and Communication" Games 12, no. 1: 24. https://doi.org/10.3390/g12010024