Limitations of spatial models of voting: Difference between revisions
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To interpret this, we consult the table once more. If there are d=4 important issues voters are using to judge candidates, then we require ''at least'' 5 candidates to potentially allow voters to account for all possible political positions in an election. This is how when only n=2 candidates exist, any further dimension or attribute will not lead to more resolution than for d=1. In other words, there is a collapse of the entire ideological space in one dimension for each voter. This is, effectively, the problem of two-party domination and single-issue voting. |
To interpret this, we consult the table once more. If there are d=4 important issues voters are using to judge candidates, then we require ''at least'' 5 candidates to potentially allow voters to account for all possible political positions in an election. This is how when only n=2 candidates exist, any further dimension or attribute will not lead to more resolution than for d=1. In other words, there is a collapse of the entire ideological space in one dimension for each voter. This is, effectively, the problem of two-party domination and single-issue voting. |
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These observations also have important implications on specific voting methods. An |
These observations also have important implications on specific voting methods. An [[Instant-runoff Voting]] election limited to top-three rankings fundamentally limits what sort of ideological distributions can be conveyed, no matter how many candidates are running. |
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From the table above, we see that if every voter is forced to rank only 3 candidates, then every voter can only express information about at most two relevant issues in their ballot<ref>There's at least one extra dimension, because a voter has to classify which are the "top three" candidates, so there has to be a "line" separating these three candidates from everyone else.</ref>, as more issues cannot ever classify the 3 ranked candidates more. Even if they are inherently ranking the candidates based on many other things, this information cannot fit into the ballot and information is fundamentally being lost. It is functionally equivalent to a scenario where voters are forced to use only two attributes to judge their candidates. |
From the table above, we see that if every voter is forced to rank only 3 candidates, then every voter can only express information about at most two relevant issues in their ballot<ref>There's at least one extra dimension, because a voter has to classify which are the "top three" candidates, so there has to be a "line" separating these three candidates from everyone else.</ref>, as more issues cannot ever classify the 3 ranked candidates more. Even if they are inherently ranking the candidates based on many other things, this information cannot fit into the ballot and information is fundamentally being lost. It is functionally equivalent to a scenario where voters are forced to use only two attributes to judge their candidates. |
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