Limitations of spatial models of voting: Difference between revisions
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However, the number of dimensions chosen for this geometric embedding imposes fundamental restrictions on the allowed number of candidates which may be effectively distinguished by the voters using ballots, as there is only a finite number of regions possible for each possible ranking assignment of candidates. Conversely, an insufficient number of candidates in a ballot (either by a small number of candidates or arbitrarily restricting the ballot) will also fundamentally restrict the effective opinion space voters can express, as the effective dimensionality is inherently reduced. |
However, the number of dimensions chosen for this geometric embedding imposes fundamental restrictions on the allowed number of candidates which may be effectively distinguished by the voters using ballots, as there is only a finite number of regions possible for each possible ranking assignment of candidates. Conversely, an insufficient number of candidates in a ballot (either by a small number of candidates or arbitrarily restricting the ballot) will also fundamentally restrict the effective opinion space voters can express, as the effective dimensionality is inherently reduced. |
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The following article discusses this limitation and some implications, both in theory and practice. The specific numerical results below assume an Euclidean space and Euclidean distances, but similar qualitative arguments apply to any spatial model and chosen metric. |
The following article discusses this limitation and some implications, both in theory and practice. The specific numerical results below assume an Euclidean space and Euclidean distances, but similar qualitative arguments apply to any spatial model and chosen metric, as well as the actual real-life behavior of voters (although quantifying it is impossible). |
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==How many ballots could voters ''actually'' cast?== |
==How many ballots could voters ''actually'' cast?== |
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