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We initiate the study of incentives in a general machine learning framework. We focus on a game-theoretic regression learning setting where private information is elicited from multiple agents with different, possibly conflicting, views on how to label the points of an input space. This conflict potentially gives rise to untruthfulness on the part of the agents. In the restricted but important case when every agent cares about a single point, and under mild assumptions, we show that agents are motivated to tell the truth. In a more general setting, we study the power and limitations of mechanisms without payments. We finally establish that, in the general setting, the VCG mechanism goes a long way in guaranteeing truthfulness and economic efficiency.

We consider a broad class of situations where a society must choose from a finite set of alternatives. This class includes, as polar cases, those where the preferences of agents are completely unrestricted and those where their preferences are single-peaked. We prove that strategy-proof mechanisms in all these domains must be based on a generalization of the median voter principle. Moreover, they must satisfy a property, to be called the "intersection property," which becomes increasingly stringent as the preference domain is enlarged. In most applications, our results precipitate impossibility theorems. In particular, they imply the Gibbard Satterthwaite theorem as a corollary.

We consider rules that choose a location on a graph (e.g. a road network) based on agents ’ single-peaked preferences. First, we characterize the class of strategy-proof, onto rules when the graph is a tree. Such a rule is based on a collection of generalized median voter rules (Moulin, 1980) satisfying a consistency condition. Second, we characterize such rules for graphs containing cycles. We show that while such a rule is not necessarily dictatorial, the existence of a cycle grants some agent an amount of decisive power, unlike the case of trees. Rules for this case can be described in terms of a subclass of such rules for trees. Journal of Economic Literature Classification

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In this paper, we characterize strategy-proof voting rules when the set of alternatives has a multi-issue structure, and the voters ’ preferences are represented by acyclic CP-nets that follow a common order over issues. We show that if the preference domain is lexicographic, then a voting rule satisfying non-imposition is strategyproof if and only if it can be decomposed into multiple strategyproof rules, one for each issue and each setting of the issues preceding it. We then prove impossibility theorems for strategy-proof voting rules that satisfy non-imposition in two kinds of preference domains: the first result is for supersets of any lexicographic preference domain, and the second is for supersets of any rich preference domain (for a notion of richness introduced by Le Breton and Sen). Categories and Subject Descriptors

Strategy-proofness, requiring that truth-telling is a dominant strategy, is a standard concept in social choice theory. However, the concept of strategy-proofness has serious drawbacks. First, announcing one's true preference may not be a unique dominant strategy, and using the wrong dominant strategy may lead to the wrong outcome. Second, almost all strategy-proof mechanisms have a continuum of Nash equilibria, and some of which produce the wrong outcome. Third, experimental evidence shows that most of the strategy-proof mechanisms do not work well. We argue that a possible solution to this dilemma is to require double implementation in Nash equilibrium and in dominant strategies, which we call secure implementation. We characterize environments where secure implementation is possible, and compare it with dominant strategy implementation. An interesting example of

Abstract We study the case where agents have preferences over ranges (intervals) of values, and we wish to elicit and aggregate these preferences. For example, consider a set of climatologist agents who are asked for their predictions for the increase in temperature between 2009 and 2100. Each climatologist submits a range, and from these ranges we must construct an aggregate range. What rule should we use for constructing the aggregate range? One issue in such settings is that an agent (climatologist) may misreport her range to make the aggregate range coincide more closely with her own (true) most-preferred range. We extend the theory of single-peaked preferences from points to ranges to obtain a rule (the median-of-ranges rule) that is strategy-proof under a condition on preferences. We then introduce and analyze a natural class of algorithms for approximately eliciting a median range from multiple agents. We also show sufficient conditions under which such an approximate elicitation algorithm still incentivizes agents to answer truthfully. Finally, we consider the possibility that ranges can be refined when the topic is more completely specified (for example, the increase in temperature on the North Pole given the failure of future climate pacts). We give a framework and algorithms for selectively specifying the topic further based on queries to agents. 1

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