We show that there are equilibria where the auction price is completely uninformative about the state of the world and aggregates no information even in an arbitrarily large auction. The good that is auctioned is a common-value object for the bidders and a bidder's valuation for the object is determined jointly by the state of the world and an action that he chooses after winning the object but before he observes the state. Before the auction, each bidder receives an informative but imperfect signal about the state of the world. We study a market where k identical and indivisible objects are allocated using a uniform-price auction where n > k bidders each demand one object. If liquidity demand is negatively correlated with the asset value, then prices in large markets aggregate all information except that contained in liquidity demand.ĭate: April 3, 2012. If liquidity demand is positively correlated (or uncorrelated) with the asset value, then prices in large markets aggregate all available information. We then use this characterization to study the informational efficiency of prices as the number of strategic traders becomes large. We show that there always exists a unique linear equilibrium, characterize it analytically, and illustrate its properties with a number of applications. We allow for essentially arbitrary correlations among the random variables involved in the model: the value of the traded asset, the signals of strategic traders and competitive market makers, and the demand from liquidity traders. Our model is based on the single-period version of the linear-normal framework of Kyle (1985). We study trading behavior and the properties of prices in informationally complex markets. The critical observation is that a vote is more likely to be pivotal for the decision if turnout is smaller, leading to a systematic bias of the decision toward the low-turnout state. Moreover, information aggregation will fail in all equilibria. Second, when the turnout is the result of costly voter recruitment by a biased organizer, the organizer can ensure that its favourite policy |$a$| is implemented with high probability independent of the state as the voter recruitment cost vanishes. In contrast to existing results for large elections, there are equilibria in which information aggregation fails whenever there is an asymmetry in turnout information aggregation is only guaranteed in all equilibria if turnout is state independent. Each recruited voter observes a private signal about the unknown state but does not learn the turnout.įirst, we characterize how the outcomes of large elections depend on the turnout pattern across states. Voters are symmetric ex ante and prefer policy a in state |$\alpha$| and policy |$b$| in state |$\beta$|, but the organizer prefers policy |$a$| regardless of the state. State-dependent turnout may arise from the actions of a biased and informed “election organizer”. We study the aggregation of dispersed information in elections in which turnout may depend on the state.
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