The Chairman’s Paradox Revisited |
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Authors: | M Braham F Steffen |
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Institution: | (1) Institute of SocioEconomics (IAW), University of Hamburg, Von-Melle-Park 5, 20146 Hamburg, Germany;(2) University of Liverpool Management School (ULMS), Chatham Street, Liverpool, L69 7ZH, UK |
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Abstract: | This paper re-examines the so-called ‘chairman’s paradox‘ that was first noticed by Farquharson in his path breaking tract
on sophisticated voting, Theory of Voting (1969). The Chairman’s paradox is concerned with the case of a three member committee in which a particular player who has
a regular and a tie-breaking vote – the ‘chairman’ – not only will do worse in specific instances under the plurality procedure
for three alternatives than if he did not have such a vote, but will also do worse overall. That is, the chairman’s a priori probability of success (‘getting what one wants’) for all possible games with linear (strict) preference orders is lower than that of the two regular members. It is demonstrated that this result, which comes
about if voters act strategically rather than sincerely, is not as robust as it has been thought to be. By merely replacing
the standard assumption of linear preference orders with weak preference orders, which allow for indifference, we can escape from the paradox for the canonical case of three players and
three alternatives. With weak preference orders, the a priori success of the chairman is now greater than that of the other two players. We also point to a new paradox of sophisticated voting. |
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