© 2010 David Gustafsson

The Condorcet Paradox

I came across an interesting concept in the previous weeks readings called the Condorcet Paradox. This states that:

If options are voted in a sequence, the options that get voted later in the sequence tends to win.

This implies that if you are in a meeting to decide something, make sure that your best option is presented as late as possible.

Let’s take an example. Table 1 presents the preferences for player 1, 2 and 3 between option A, B and C. 1 the strongest preference and 3 the weakest.

Option A Option B Option C
Player 1 1 2 3
Player 2 2 3 1
Player 3 3 1 2

Table 1. Different preferences in outcome.

Assume two sequences;

a) Option A vs. Option B = 2-1; Winner (A) vs. Option C = 1-2. Winner is C

b) Option A vs. Option C = 1-2; Winner (C) vs. Option B = 1-2. Winner is B

Further on the impossibility theorem states that it is impossible to guarantee maximisation of group preference when putting together preferences from three or more individuals on three or more options.

The order the issues are raised in a meeting/negotiation/decision situation determines the outcome. One other reason for this could be that humans often make the assumption that if A gives B and B gives C, then A must also give C. This is however not always the case outside mathematics.

It is easy to find cases when the sequence does not affect the outcome. Say that C is better than both A and B. However there is never a case where it is beneficial to start voting on an option early. The more comparisons that are made the bigger is the likelihood that an early option looses a comparison and is out of the game.

Reference

Thompson, L. L. (2005) Chapter 9. Multiple parties, coalitions and teams. IN Thompson, L. L. (Ed.) The mind and heard of the negotiator. 3rd ed.