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The Reconstruction of an Election under Alternative Rules

Abstract

In this chapter we offer an interlude from the purely theoretical results of Chapters 2 and 3. This break serves not only the purpose of making this theory less austere and perhaps more palatable but also shows how the theory can be wedded to reality. Although the results so far established do not apply, strictly speaking, to elections that run more than two ballots, some of the analysis of runoff elections in the previous chapter can be adapted to more extended elimination contests.

Keywords

Vote System Strategic Vote Approval Vote Probable Winner Alternative Rule 
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Footnotes to Chapter 4

  1. 1.
    This chapter is based largely on Steven J. Brams and Peter C. Fishburn, “Reconstructing Voting Processes: The 1976 House Majority Leader Election,” Political Methodology, 7, 3–4 (1981), 95–108.Google Scholar
  2. 2.
    Bruce I. Oppenheimer and Robert L. Peabody, “The House Majority Leader Contest, 1976” (mimeographed, 1977); B. I. Oppenheimer and R. L. Peabody, “How the Race for Majority Leader Was Won—by One Vote,” Washington Monthly 9 (November 1977), 46–56.Google Scholar
  3. 3.
    B. I. Oppenheimer and R. L. Peabody, “How the Race for Majority Leader Was Won—by One Vote,” Washington Monthly 9 (November 1977), 47.Google Scholar
  4. 4.
    James M. Naughton, “4 Seeking House Leadership Press Claims in the Election Today,” New York Times, December 6, 1976, pp. 1, 28.Google Scholar
  5. 5.
    David E. Rosenbaum, “O’Neill Is Speaker, Rep. Wright of Texas Wins Majority Post,” New York Times, December 7, 1976, pp. 1, 33.Google Scholar
  6. 6.
    B. I. Oppenheimer and R. L. Peabody, “How the Race for Majority Leader Was Won—by One Vote,” Washington Monthly 9 (November 1977), 47.Google Scholar
  7. 7.
    B. I. Oppenheimer and R. L. Peabody, “The House Majority Leader Contest, 1976” (mimeographed, 1977).Google Scholar
  8. 8.
    B. I. Oppenheimer and R. L. Peabody, “How the Race for Majority Leader Was Won—by One Vote,” Washington Monthly 9 (November 1977), 53.Google Scholar
  9. 9.
    B. I. Oppenheimer and R. L. Peabody, “How the Race for Majority Leader Was Won—by One Vote,” Washington Monthly 9 (November 1977), 54.Google Scholar
  10. 10.
    A full explanation of this and the related condition of “value restrictedness,” with examples, is given in Steven J. Brams, Paradoxes in Politics: An Introduction to the Nonobvious in Political Science (New York: Free Press, 1976), pp. 37–41; see also Peter C. Fishburn, The Theory of Social Choice (Princeton: Princeton University Press, 1973), pp. 100–144. Singlepeakedness means, roughly, that there exists a single dimension underlying the preferences of voters (e.g., a liberalism-conservatism scale) along which alternatives (e.g., candidates) can be ordered. Single-peaked preferences preclude the existence of a paradox of voting. This constraint on individual preferences was originally noted by Francis Galton, “One Vote, One Value,” Nature 75 (February 28, 1907), 414, and discussed extensively in Duncan Black, The Theory of Committees and Elections (Cambridge: Cambridge University Press, 1958), pp. 14–35.Google Scholar
  11. 11.
    B. I. Oppenheimer and R. L. Peabody, “How the Race for Majority Leader Was Won—by One Vote,” Washington Monthly 9 (November 1977), 56.Google Scholar
  12. 12.
    Mary Russell, “Representative Wright Is Elected House Majority Leader,” Washington Post, December 7, 1976, pp. A1, A6.Google Scholar
  13. 13.
    B. I. Oppenheimer and R. L. Peabody, “How the Race for Majority Leader Was Won—by One Vote,” Washington Monthly 9 (November 1977), 53–54.Google Scholar
  14. 14.
    Kenneth A. Shepsle (personal communication to S. J. Brams, November 14, 1978).Google Scholar

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© Springer Science+Business Media, LLC 2007

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