Tacit co-operation in three-alternative non-cooperative voting games: A new model of sophisticated behaviour under the plurality procedure

Two models, one due to Farquharson and the other to Niemi-Frank, attempt to account for sophisticated voting behaviour when the voters' preference orderings are common knowledge and communication among Voters is impossible. Having subjected these two models to experimental testing, we have found them lacking. Hence, we propose a new model of sophisticated voting for 3-alternative n-person non-cooperative games under the plurality procedure, which can be extended to other voting procedures and more than three alternatives.The model assumes that voters whose first preference is (one of) the Condorcet winner(s) will (tacitly) co-ordinate their strategies and vote for their first preference, and specifies the conditions under which voters whose second preference is (one of) the Condorcet winner(s) will vote for their second (rather than their first) preference. Consequently, our model predicts that: (i) if there is a single Condorcet winner he or she will be elected; (ii) if there is more than one Condorcet winner the final outcome will be a tie between them; and (iii) when there are cyclical majorities with a single maximin alternative, this alternative will be elected.