Disclaimer. Don't rely on these old notes in lieu of reading the literature, but they can jog your memory. As a grad student long ago, my peers and I collaborated to write and exchange summaries of political science research. I posted them to a wiki-style website. "Wikisum" is now dead but archived here. I cannot vouch for these notes' accuracy, nor can I even say who wrote them. If you have more recent summaries to add to this collection, send them my way I guess. Sorry for the ads; they cover the costs of keeping this online.
Feddersen and Sandroni. 2002. A theory of participation in elections.
This is overly simple, but here's the basic idea: The turnout game generates endogenous payoffs for doing your part--in other words, a payoff for doing your duty by voting. In essence, we all are conditional cooperators; I'll vote if you vote, and this is our civic duty. I get an extra payoff from cooperating with this duty.
Since we recognize that voting is costly, and that our coalition (party) only needs a certain number of vote to win, we coordinate on some cutoff point; those for whom voting is more costly than this cutoff do not vote, and those for whom voting is less costly than this cutoff do vote. The cutoff will be a bit lower for the minority coalition than for the majority coalition (so a slightly higher proportion of the losing coalition will turn out).
So basically, this is an argument asserting that civic duty is group based.
Feddersen and Sandroni model "A two-candidate election in which a large population of agents may vote for candidate 1, vote for candidate 2, or abstain. Voting costs vary within the population and a single vote is never pivotal" (4). Note that the non-pivotal aspect of their model differs substantially from most rational choice accounts.
A rule-utilitarian is defined as "An agent who receives a payoff for acting according to a strategy profile (a rule)" (3). Harsanyi (1992) links this conception to the maximization of social welfare. Feddersen and Sandroni drop this assumption because of the problems it creates--i.e. people disagree about which candidate will maximize social welfare. Instead, they assume the endogeneity of preferences.
There are two types of rule-utilitarian agents in Feddersen and Sandroni's model. Some prefer candidate 1 and others prefer candidate 2. An agent's type is endogenously determined, and "Each agent has an action he should take and receives an additional payoff from taking this action" (4). The endogeneity assumption reflects the reality that self-interest, religion, sense of social justice, etc... can determine one's preferences. The payoff derives from the agent's sense of "doing their part" (11). Ethical agents receive a payoff for doing their part. Abstainers receive no payoff for doing their part.
A rule defines "how each agent should behave (i.e. a rule is an arbitrary mapping from voting costs to the action space)" (4). The agent's choice of a rule is determined by his or her preference type. That is, agents "rank rules according to their preferences" (5).
An agent's behavior profile is consistent if his or her behavior "follows from the agent's preferred rule" (5). Feddersen and Sandroni claim that "If agents' behavior is consistent then there exists a cutoff point for each type such that agents with voting costs below this threshold should (and will) vote for their favored candidate. Agents with voting costs above the threshold abstain" (5).
(Note: This is the derived voting rule. We all want "enough" people from our coalition to vote, but we don't want everybody from our coalition to vote, since that will be wasteful. So we have a rule that people vote if their costs are under a certain cutoff.)
The model assumes that "Fixing the probability candidate 1 wins the election, all agents prefer lower turnout since it produces lower social costs" (13).
After using some (quite technical) game theory, the authors present the following results: "The fraction of voters in the minority group who participate in the election is greater than the fraction in the majority, but the majority has a higher chance of winning the election...Expected turnout goes to zero as the level of disagreement vanishes...Expected turnout is increasing in the importance of the election and the expected margin of victory is decreasing on the level of disagreement" (33).
It seems that the endogenous preferences assumed in the model cannot account for strategic voting. Their model only accounts for a two-candidate race, and has nothing to say about the voting behavior of members of small third-parties. In addition, the agents' preference for lower turnout seems unrealistic. Do people really care that much about whether too many people vote? Reality seems to confirm that people like high turnout, if anything. The authors comment on this issue on page 13, but their explanation seems pretty weak. I don't think that I am alone in believing that the "social cost" of an overdetermined outcome in an election is negligible.
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