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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Footnotes to Chapter 4
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.
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.
B. I. Oppenheimer and R. L. Peabody, “How the Race for Majority Leader Was Won—by One Vote,” Washington Monthly 9 (November 1977), 47.
James M. Naughton, “4 Seeking House Leadership Press Claims in the Election Today,” New York Times, December 6, 1976, pp. 1, 28.
David E. Rosenbaum, “O’Neill Is Speaker, Rep. Wright of Texas Wins Majority Post,” New York Times, December 7, 1976, pp. 1, 33.
B. I. Oppenheimer and R. L. Peabody, “How the Race for Majority Leader Was Won—by One Vote,” Washington Monthly 9 (November 1977), 47.
B. I. Oppenheimer and R. 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), 53.
B. I. Oppenheimer and R. L. Peabody, “How the Race for Majority Leader Was Won—by One Vote,” Washington Monthly 9 (November 1977), 54.
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.
B. I. Oppenheimer and R. L. Peabody, “How the Race for Majority Leader Was Won—by One Vote,” Washington Monthly 9 (November 1977), 56.
Mary Russell, “Representative Wright Is Elected House Majority Leader,” Washington Post, December 7, 1976, pp. A1, A6.
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.
Kenneth A. Shepsle (personal communication to S. J. Brams, November 14, 1978).
Rights and permissions
Copyright information
© 2007 Springer Science+Business Media, LLC
About this chapter
Cite this chapter
(2007). The Reconstruction of an Election under Alternative Rules. In: Approval Voting. Springer, New York, NY. https://doi.org/10.1007/978-0-387-49896-6_4
Download citation
DOI: https://doi.org/10.1007/978-0-387-49896-6_4
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-49895-9
Online ISBN: 978-0-387-49896-6
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)