Measures of Agreement in Voters’ Preferences
The impact that adding varying degrees of internal structure to voters’ preferences has on the probability of observing Condorcet’s Paradox is considered, by defining the restrictions on voters’ preferences on candidates so that the electorate is behaving in accord with each of several models of rational behavior. Proximity measures are introduced to determine the minimum proportion α of voters’ preference rankings that must be ignored for the remaining voters to have preferences that are in perfect agreement with each of the models of restricted preferences. While it is expected that the probability of observing Condorcet’s Paradox should consistently change as α increases, this outcome is not observed for all of the models. The strongest consistent relationship is found to exist for those models that are based on group mutual coherence that assume that voters can mutually agree on an underlying ordering of candidates along a common dimension.
- Arrow, K. J. (1963). Social choice and individual values (2nd ed.). New Haven CT: Yale University Press.Google Scholar
- Black, D. (1958). The theory of committees and elections. Cambridge: Cambridge University Press.Google Scholar
- Buchanan, J. M. (1970). The public finances. Homewood, IL: Richard D Irwin Press.Google Scholar
- Gehrlein, W. V. (2006). Condorcet’s paradox. Berlin: Springer Publishing.Google Scholar
- Gehrlein, W. V., Lepelley, D., & Plassmann, F. (2016b). To rank or not to rank: A summary. Note at: www.researchgate.net/publication/306276950_To_Rank_or_Not_to_Rank_A_Summary.