Ebook: Voting Paradoxes and Group Coherence: The Condorcet Efficiency of Voting Rules

The likelihood of observing Condorcet's Paradox is known to be very low for elections with a small number of candidates if voters’ preferences on candidates reflect any significant degree of a number of different measures of mutual coherence. This reinforces the intuitive notion that strange election outcomes should become less likely as voters’ preferences become more mutually coherent. Similar analysis is used here to indicate that this notion is valid for most, but not all, other voting paradoxes. This study also focuses on the Condorcet Criterion, which states that the pairwise majority rule winner should be chosen as the election winner, if one exists. Representations for the Condorcet Efficiency of the most common voting rules are obtained here as a function of various measures of the degree of mutual coherence of voters’ preferences. An analysis of the Condorcet Efficiency representations that are obtained yields strong support for using Borda Rule.

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The likelihood of observing Condorcet's Paradox is known to be very low for elections with a small number of candidates if voters’ preferences on candidates reflect any significant degree of a number of different measures of mutual coherence. This reinforces the intuitive notion that strange election outcomes should become less likely as voters’ preferences become more mutually coherent. Similar analysis is used here to indicate that this notion is valid for most, but not all, other voting paradoxes. This study also focuses on the Condorcet Criterion, which states that the pairwise majority rule winner should be chosen as the election winner, if one exists. Representations for the Condorcet Efficiency of the most common voting rules are obtained here as a function of various measures of the degree of mutual coherence of voters’ preferences. An analysis of the Condorcet Efficiency representations that are obtained yields strong support for using Borda Rule.

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The likelihood of observing Condorcet's Paradox is known to be very low for elections with a small number of candidates if voters’ preferences on candidates reflect any significant degree of a number of different measures of mutual coherence. This reinforces the intuitive notion that strange election outcomes should become less likely as voters’ preferences become more mutually coherent. Similar analysis is used here to indicate that this notion is valid for most, but not all, other voting paradoxes. This study also focuses on the Condorcet Criterion, which states that the pairwise majority rule winner should be chosen as the election winner, if one exists. Representations for the Condorcet Efficiency of the most common voting rules are obtained here as a function of various measures of the degree of mutual coherence of voters’ preferences. An analysis of the Condorcet Efficiency representations that are obtained yields strong support for using Borda Rule.
Content:
Front Matter....Pages i-xii
Voting Paradoxes and Their Probabilities....Pages 1-47
Condorcet’s Paradox and Group Coherence....Pages 49-79
Other Incompatibility Paradoxes....Pages 81-121
Other Voting Paradoxes....Pages 123-155
Condorcet Efficiency and Social Homogeneity....Pages 157-198
Coherence and the Efficiency Hypothesis....Pages 199-247
Other Characteristics of Voting Rules....Pages 249-294
The Significance of Voting Rule Selection....Pages 295-329
Complete PMR Ranking Efficiencies....Pages 331-366
Back Matter....Pages 367-385

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The likelihood of observing Condorcet's Paradox is known to be very low for elections with a small number of candidates if voters’ preferences on candidates reflect any significant degree of a number of different measures of mutual coherence. This reinforces the intuitive notion that strange election outcomes should become less likely as voters’ preferences become more mutually coherent. Similar analysis is used here to indicate that this notion is valid for most, but not all, other voting paradoxes. This study also focuses on the Condorcet Criterion, which states that the pairwise majority rule winner should be chosen as the election winner, if one exists. Representations for the Condorcet Efficiency of the most common voting rules are obtained here as a function of various measures of the degree of mutual coherence of voters’ preferences. An analysis of the Condorcet Efficiency representations that are obtained yields strong support for using Borda Rule.
Content:
Front Matter....Pages i-xii
Voting Paradoxes and Their Probabilities....Pages 1-47
Condorcet’s Paradox and Group Coherence....Pages 49-79
Other Incompatibility Paradoxes....Pages 81-121
Other Voting Paradoxes....Pages 123-155
Condorcet Efficiency and Social Homogeneity....Pages 157-198
Coherence and the Efficiency Hypothesis....Pages 199-247
Other Characteristics of Voting Rules....Pages 249-294
The Significance of Voting Rule Selection....Pages 295-329
Complete PMR Ranking Efficiencies....Pages 331-366
Back Matter....Pages 367-385
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