Aggregating value ranges: preference elicitation and truthfulness

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]  Yoav Shoham,et al.  Combinatorial Auctions , 2005, Encyclopedia of Wireless Networks.

[2]  M. Satterthwaite.  Strategy-proofness and Arrow's conditions: Existence and correspondence theorems for voting procedures and social welfare functions , 1975 .

[3]  Vincent Conitzer,et al.  Determining Possible and Necessary Winners under Common Voting Rules Given Partial Orders , 2008, AAAI.

[4]  Tuomas Sandholm,et al.  Preference elicitation in combinatorial auctions , 2002, EC '01.

[5]  Peter Haddawy,et al.  Toward Case-Based Preference Elicitation: Similarity Measures on Preference Structures , 1998, UAI.

[6]  Daphne Koller,et al.  Making Rational Decisions Using Adaptive Utility Elicitation , 2000, AAAI/IAAI.

[7]  Toby Walsh,et al.  Incompleteness and Incomparability in Preference Aggregation , 2007, IJCAI.

[8]  Toby Walsh,et al.  Aggregating partially ordered preferences: impossibility and possibility results , 2005, TARK.

[9]  Kim C. Border,et al.  Straightforward Elections, Unanimity, and Phantom Voters , 1983 .

[10]  Toby Walsh,et al.  Strategic voting when aggregating partially ordered preferences , 2006, AAMAS '06.

[11]  Toby Walsh,et al.  Aggregating Partially Ordered Preferences , 2009, J. Log. Comput..

[12]  Vincent Conitzer.  Eliciting single-peaked preferences using comparison queries , 2007, AAMAS '07.

[13]  Craig Boutilier,et al.  Local Utility Elicitation in GAI Models , 2005, UAI.

[14]  Yuval Shahar,et al.  Utility Elicitation as a Classification Problem , 1998, UAI.

[15]  D. Black.  On the Rationale of Group Decision-making , 1948, Journal of Political Economy.

[16]  Peter Haddawy,et al.  Problem-Focused Incremental Elicitation of Multi-Attribute Utility Models , 1997, UAI.

[17]  Craig Boutilier,et al.  A POMDP formulation of preference elicitation problems , 2002, AAAI/IAAI.

[18]  A. Gibbard.  Manipulation of Voting Schemes: A General Result , 1973 .

[19]  Vincent Conitzer,et al.  Communication complexity of common voting rules , 2005, EC '05.

[20]  Salvador Barberà,et al.  Strategy-proof voting on compact ranges , 1998 .

[21]  Georg Dengler.  N.F. [1.] , 1873 .

[22]  Vincent Conitzer,et al.  Vote elicitation: complexity and strategy-proofness , 2002, AAAI/IAAI.

[23]  Tuomas Sandholm,et al.  Preference elicitation in combinatorial auctions , 2001, AAMAS '02.