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Limitations of spatial models of voting: Difference between revisions

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Limitations of spatial models of voting (view source)

Revision as of 08:20, 11 February 2023

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m (RobLa moved page Dimensional limitations of the spatial model to Limitations of spatial models of voting: There is more than one spatial model, and the limitations may be more than dimensional. Those limitations should be added to this article.)
(Split up the introduction, and removed the banner)
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"[[Spatial model of voting]]"are ubiquitous in theoretical study and simulations of voting methods. This article describes many '''limitations of spatial models of voting'''.
{{rename|from=Dimensional limitations of the spatial model|to=Limitations of the spatial model|date=January 2023}}
 
[[Spatial model of voting|Spatial models]] are ubiquitous in theoretical study and simulations of voting methods. In thesespatial models of agent behavior, agents (e.g. voters, candidates) are placed in an abstract geometric space, usually Euclidean, in which each dimension denotes some ideological alignment or opinion on an issue. The behavior of agents is modeled by how "close" (under some appropriate metric) they are to other agents in this space. In the context of voting, voters are modelled as ranking candidates depending on their proximity within this space.
 
However, models based too strictly on geometric representations have challenges representing both voters and candidates. This article describes some of the challenges.
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.▼
 
== Number of dimensions ==
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).▼
▲However, theThe number of dimensions chosen for this geometric embedding imposes fundamental restrictions on the allowed number of candidates. There is a limited number of dimensions whichthat 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.
 
▲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).
 
==How many ballots could voters ''actually'' cast?==
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