ECON 451: Public Choice
Professor Peter Coughlin


Voting Paradoxes

Our main references are:

1) Jerry S. Kelly, Social Choice Theory: An Introduction

Chapter 2 - The Voting Paradox (pages 15 through 17)

2) Allan M. Feldman & Roberto Serrano, Welfare Economics and Social Choice Theory, 2nd Edition.

[1] From "The most important..." in the 7th line of the 1st paragraph of the section "The Concerns of Social Choice" (on p. 4) through "...better than B?" at the end of the 3rd-from-last paragraph on p. 5
[2] From the beginning of Chapter 1 (on p. 11) through "... individuals' preferences. " at the end of the last full paragraph on p. 12
[3] From the beginning of the section "The Formal Model of Preferences" (on p. 14) through "... is acyclic." at the end of Proposition 1 on p. 15
[4] From the beginning of the section "Introduction to Social Preferences" (on p. 24) through "... individual preferences." in the 2nd sentence in the last full paragraph on p. 25

3) A. Taylor & A. Pacelli, Mathematics and Politics, 2nd edition

[1] From "Social Choice Procedure 1 ..." at the top of p.6 through "... Condorcet's method is used" at the end of the 4th paragraph on that page,
[2] From "Example: ..." near the bottom of p. 8 through "... with Condorcet's method." at the end of the 2nd paragraph on p.9 and
[3] From "... the simplest example" in the second line on p.21 through "... 2 to 1)." in the last line before Proposition 2.

The following items are recommended readings (which supplement the main readings):


Sherif El-Helaly, The Mathematics of Voting and Apportionment, Springer, 2019.

[1] From the beginning of Section 1.3 (on page 21) through "... y one-to-one)." in the eighth line of the section;

[2] From the beginning of Subsection 1.3.1 (on page 21) through the end of Subsection 1.3.2 (on page 24).


Jean Hendriks & Gareth D. Myles, Intermediate Public Economics, 2ndedition, The MIT Press, 2013.

[1] Section 11.3, starting on pg. 347, in 3rd paragraph at "case of 3 voters..." through 4th paragraph and

[2] Section 11.4.2, starting on pg. 351 to the end of the section


Jonathan K. Hodge & Richard E. Klima, The Mathematics of Voting and Elections, 2nd edition, American Mathematical Society, 2018.

[1] The definition of a "Condorcet winner" that is near the bottom of page 35

[2] From The beginning of Question 3.4 on p. 36 through "Condorcet winner" in part (d) of the question


All of these items are available through Course Reserves at ELMS.