Limitations of spatial models of voting: Difference between revisions
Limitations of spatial models of voting (view source)
Revision as of 17:48, 6 January 2023
, 1 year ago→Dimensional resolution of a ballot
(Created page with "The spatial model is ubiquitous in theoretical study and simulations of voting methods. However, the dimension of this geometric embedding imposes fundamental restrictions on the allowed number of candidates which may be distinguished, as there is a finite number of regions possible for each possible ranking. The following article discusses this limitation and some implications. == How many ballots could voters ''actually'' cast? == With <ma...") |
|||
Line 59:
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.
The population as a whole can cast <math>\binom{n}{d}</math> ballots, which means the voting method "mixes" the information multiple voters expressed, as each voter is using different attributes in their ballots. Thus, there
== Simulations ==
| |||