Condorcet Paradox

Network Capital
The Condorcet Paradox explores the cyclic nature of social choice even when the individual choice is transitive. That is, an individual might prefer candidate X to candidate Y, candidate Y to candidate Z and candidate Z to candidate X. Yet pick X or Z, and not Y. This is because conflicting majorities do not have an identify order of candidate preference.

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In electoral or voting system where choices are non-binary the Condorcet Paradox appears. Instances where voters have more than two options to choose from, the electoral results are largely inconsistent and non-representative of individual preferences.

First noted by Marquis de Condorcet in the late 18th century, the Condorcet Paradox is a social choice theory. It states that despite having transitive individual choices, the social choice will be cyclic. The Condorcet Paradox is best explained with a thought experiment with three candidates A, B and C contesting elections, and three voters X, Y and Z voting. The experiment assumes that voter X’s order of candidate preference is A, B and then C; for voter Y it is B, C and then A; and for voter Z it is C, A and B. In such a case, regardless of which candidate wins, two-third of the electorates’ preference would not be accounted for.

Using the Condorcet Paradox, pollsters attempt to model actual election outcomes. This is done by extrapolating real data and modelling voting behaviour. Along with being a useful tool in predicting electoral results, the Condorcet Paradox is also a testament to the limitations of voting process. It has led to several voting reforms like two-stage voting process, enlarged electorates to limit the impact of the Condorcet Paradox, and cultural (and identity-based) impact on voting behaviours.
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