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. [ABSTRACT FROM AUTHOR]