Choosing the level of a public good when agents have an outside option

Abstract

The work examines strategy-proof social choice functions which select a level or the location of a public good when its consumption is not compulsory. We assume that agents have single-peaked preferences on the consumption of the public good as well as a reservation utility. Agents opt out of the good whenever they get a utility smaller than their reservation utility. We characterize strategy-proof and efficient social choice functions as well as the ones which are anonymous and group strategy-proof. Finally, we observe that for given preferences a Condorcet winner may not exist. Copyright Springer-Verlag 2004

Computational aspects of strategic behaviour in elections with top-truncated ballots

“…However, this property no longer holds when top-truncated votes are allowed. As has also been pointed out by Cantala [10], it is not even necessary that a weak-Condorcet winner exists in such settings. We illustrate this with the following example.…”

“…The notion of single-peaked preferences was introduced by Black [7] and subsequently there has been a lot of work in the social choice literature on the same. Among these, in particular, we note the work of Cantala [10] who introduced the concept of "single-peaked with outside options" which is similar to the notion of single-peaked with top-truncated ballots that we study here in Chapter 4, and the work of Barberá who discussed how properties of different variants of single-peaked preferences change for varying amounts of indifference permitted [1].…”

“…In social choice theory, this notion of single-peaked with toptruncated preferences has been captured as "single-peaked with outside options" in the context of choosing a level of public good by Cantala [10]. While the single-peaked model has been extensively studied and has been broadly considered as a useful model for capturing a number of important scenarios like the U.S. presidential elections and elections in committees (see for e.g.…”

Strategic requirements with indifference: single-peaked versus single-plateaued preferences

“…Cantala (2004) analyzes the particular subclass of weakly single-peaked preferences where one plateau at the lowest feasible level of utility is considered in both sides of the peak. He obtains the extreme minmax rules (a subclass of minmax rules whose outcome is always an agent's peak) as the unique strategy-proof and e¢ cient rules.…”

Two necessary conditions for strategy-proofness: On what domains are they also sufficient?

“…For example, the preferences used in Cantala (2004) when choosing a level of public good where agents' preferences are single-peaked but having an outside option, or in Miyagawa (2001), Barberà and Beviá (2002), and Ehlers (2002b) where the location of two (or more) public facilities is analyzed, are not intertwined domains.…”