Limitations of spatial models of voting: Difference between revisions
Content added Content deleted
| Line 68: | Line 68: | ||
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. |
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. |
||
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 |
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 further. 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. |
||
If ranked ballots are constrained to <math>k</math> out of <math>n</math> candidates, the population, as a whole, can only cast <math>\frac{n!}{(n-k)!}</math> ballots, which means the voting method "mixes" the information multiple voters expressed, as each voter is using a different subset of attributes in their ballots. Thus, there are no guarantees all the voters are expressing information about the same issues in their ballots, and the ballots cease to be informationally commensurable, even in principle. In effect, we are left to simply hope that their priorities are, on average, similar, as to restore commensurability. |
If ranked ballots are constrained to <math>k</math> out of <math>n</math> candidates, the population, as a whole, can only cast <math>\frac{n!}{(n-k)!}</math> ballots, which means the voting method "mixes" the information multiple voters expressed, as each voter is using a different subset of attributes in their ballots. Thus, there are no guarantees all the voters are expressing information about the same issues in their ballots, and the ballots cease to be informationally commensurable, even in principle. In effect, we are left to simply hope that their priorities are, on average, similar, as to restore commensurability. |
||