Sophisticated voting under the plurality procedure: A test of a new definition
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The Niemi-Frank definition of sophisticated voting can now be evaluated on two grounds. First, we can compare our definition to Farquharson's. For the most part, the two definitions yield identical outcomes. Both pickCondorcet winners a very high proportion of the time and prevent the selection of Condorcet losers. The major differences are in the logic underlying the two definitions and in the rate of determinacy of outcomes. Here there is a tradeoff. The logic underlying the Farquharson model is especially persuasive, although it is our feeling that the Niemi-Frank definition comes closer to mirroring the way in which voters might actually analyze a plurality situation. In any case, the price paid by the Farquharson definition for its ironclad logic is a much higher rate of indeterminacy. In over half of the cases, the Farquharson logic fails to lead to any conclusion whatsoever. The Niemi-Frank definition yields many more determinate situations, with mostly Condorcet winners and with strategies that make good, if not completely unassailable sense.
A second way of evaluating the Niemi-Frank definition is in comparison with sincere voting. A commonly-cited shortcoming of plurality voting is that often fails to choose a Condorcet winner. As we notedearlier, sophisticated plurality voting, unlike binary voting, is imperfect in this respect. Nonetheless, even taking account of the indeterminacy thatremains in the Niemi-Frank definition, sophisticated voting picked a Condorcet winner about 10 percent more frequently than did sincere voting as well as eliminating the possibility of a Condorcet loser being chosen. By this measure, the Niemi-Frank definition is not only acceptable but suggests that this form of strategic behavior actually leads tobetter outcomes.
By proposing and now by testing a new definition of sophisticated voting under plurality rule, we have begun to make some headway on understanding strategic behavior and its effects in an outwardly simple yet deceptively complex voting system. We are, of course, far from finished. Most significantly, our definition applies to only three alternatives, and Farquharson's (even if one is willing to live with its high indeterminacy) becomes extraordinarily cumbersome with more than three alternatives? In any event, the results of this foray into sophisticated nonbinary voting suggests once again that strategic behavior, rather than making things worse, improves the chances that the outcome will be the one most favored by the majority criterion.
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