The Swing Voter's Curse*October 1995Forthcoming American Economic ReviewAbstractWe analyze two-candidate elections in which some voters are uncertain about the realizationof a state variable that affects the utility of all voters.. We demonstrate the existence of a swingvoter's curse: less informed indifferent voters strictly prefer to abstain rather than vote for eithercandidate even when voting is costless. The swing voter's curse leads to the equilibrium resultthat a substantial fraction of the electorate will abstain even though all abstainers strictly prefervoting for one candidate over voting for another.Timothy J. FeddersenWolfgang Pesendorfer1In the 1994 State of Illinois elections there were 6,119,001 registered voters. Amongthose registered to vote only 3,106,566 voted in the gubernatorial race and only 2,144,200 votedon a proposed amendment to the state constitution.1 There is nothing exceptional about the levelof participation in the 1994 Illinois elections. As in most large elections in the United States, asubstantial fraction of the registered electorate abstained from voting at all and of those who didvote a substantial fraction rolled off, i.e., did not vote on every item listed on the ballot.2While abstention and roll-off are ubiquitous features of elections together they pose achallenge to positive political theory. One obvious explanation of abstention is costs to vote.However if voting is costly, since it is extremely unlikely that one person's vote changes theoutcome, it is difficult to understand why so many people vote. Conversely, if voting is notcostly, the problem is to explain why so many people abstain. This is "the paradox of not-voting".3 The solution proposed by Anthony Downs (1957) and by William H. Riker and Peter C.Ordeshook (1968)4 is that perhaps voting is costly for some citizens but not for others. Thisexplanation for participation patterns runs into trouble however as an explanation for roll-off.Presumably most of the costs to vote are associated with getting to the polls. Roll-off occurswhen voters who are already at the polls decide not to vote on a race or issue. One way that acost theory of voting might explain roll-off is by ballot position. Voters get tired of voting anddecline to vote on issues down the ballot. This explanation does not work for the example givenabove because in Illinois consititutional proposals appear first on the ballot.5A useful theory of participation must explain not only abstention and roll-off but mustalso be consistent with the well known stylized fact that better educated and informed individualsare more likely to participate than the less well educated and informed.6 In their seminal book,Who Votes, Raymond E. Wolfinger and Stephan J. Rosenstone (1980), using 1972 Bureau ofCensus data and controlling for a variety of demographic attributes including income, predict thatevery additional 4 years of schooling increases the liklihood of voting by between 4 and 13percentage points (see table 2.4 page 26). We do not dispute the proposition that costs to vote2influence participation. Our contribution here is to demonstrate that informational asymmetriesmay also influence both participation and vote choice independent of costs to vote and pivotprobabilities. We show that less informed voters have an incentive to delegate their vote viaabstention to more informed voters.We use the insight underlying the "winner's curse"7 in the theory of auctions to show thatrational voters with private information may choose to abstain or even vote for a candidate thatthey consider inferior based on their private information alone. The paradigmatic example of thewinner's curse is as follows. A group of bidders have private information about the value of an oillease and each knows that other agents have private information as well.8 If every bidder offershis expected evaluation determined from their private information the winning bidder has bid toomuch because, by virtue of winning, it follows that every other bidder's expected valuation islower. Thus, the private information of the winning bidder is a biased estimate of the true valueof the lease. The solution to the winner's curse is for every bidder to condition his offer not onlyon private information but also on what must be true about the world if his is the high bid and tobid less than they would if they were the only bidder.There is an analog to the winner's curse in elections with asymmetric information: the swingvoter's curse. A swing voter is an agent whose vote determines the outcome of an election. Bothin auctions and in elections an agent's action only matters in particular circumstances: when anagent is the high bidder in an auction or when an agent is a swing voter in an election. In eithercase, when some agents have private information that may be useful to an agent, the agent mustcondition his action not only on his information but also on what must be true about the world ifthe agent's action matters.Consider the following example. There are two candidates, the status quo (candidate 0) andthe alternative (candidate 1). Voters are uncertain about the cost of implementing the alternative.This cost is either high (state 0) or low (state 1). All voters prefer the status quo if the cost is highand the alternative if the cost is low. At least one of the voters is informed and knows the costswith certainty. However, voters do not know the exact number of informed voters in the3electorate. All of the uninformed voters share a common knowledge prior that with .9 probabilitythe cost is high and the status quo is the best candidate.Suppose that all voters (informed and uninformed alike) vote only on the basis of theirupdated prior. All of the informed voters vote for the status quo if the cost is high and thealternative if the cost is low while all of the uninformed voters vote for the status quo in bothstates. The informed voters are behaving rationally while the uninformed are not. An uninformedvoter is only pivotal if some voters have voted for the alternative. But this can only occur if thecost is low and the informed voters vote for the alternative. Therefore, an uninformed voter canaffect the election outcome only if the cost is low. Consequently, an uninformed voter should votefor the alternative. On the other hand, it cannot be rational for all uninformed voters to vote forthe alternative. In this case each uninformed voter would prefer