Who ought to be elected and who is actually elected? An empirical investigation of 92 elections under three procedures

Abstract Three voting procedures—Borda's Count (BR), Plurality Voting (PV), and the Single Transferable Vote (STV)—are compared with one another in relation to the outcomes of 92 real elections conducted in Britain by various trade unions, professional associations, and non-profit organizations. Given the social preference ordering (SPO) among the n competing candidates, of whom m candidates must be elected ( n > m ⩾ 1), each of these procedures is evaluated by means of two new indices that measure the discrepancy between the m candidates elected and the prescription of the majoritarian principle. For two of these procedures (PV and STV), we also investigate the relative frequency with which they display the recently discovered Discontinuity Paradox, namely, cases where a candidate who would be elected when m candidates must be elected would not also be elected, ceteris paribus , if m + 1 candidates were to be elected. Our analysis supports the following three conclusions: 1. (i) When m = 1, STV (or rather its Alternative Vote variant) conforms better with the SPO than do the other two procedures, particularly PV. 2. (ii) When m > 1, BR conforms with the SPO significantly better than do the other two procedures, particularly STV. 3. (iii) PV is likely to display the Discontinuity Paradox more often than STV. Since BR is not susceptible to the Discontinuity Paradox, we conclude that, in terms of avoiding this paradox and conforming with the SPO, BR performs better than both PV and STV.

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