User:Lucasvb/An upgrade to the spatial model of voters: Difference between revisions
User:Lucasvb/An upgrade to the spatial model of voters (view source)
Revision as of 09:01, 7 March 2020
, 4 years ago→Benefits & remarks
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== Benefits & remarks ==
One major benefit of this approach is that we now have a direct way to embed mutual importance into our model of voters, as well as a notion of "fuzziness" to the opinions. The width of the distribution can be used as a proxy for a voter's willingness to compromise or make sacrifices on an issue.
A low-importance opinion is a wider distribution, which means it has a smaller distance to other opinions than a sharp one. So a voter with a low-importance on an issue effectively sees that axis as "compressed", that is, distances are shorter along that axis. On the other hand, if a voter has a high importance on an issue they will perceive differences more aggressively, making them see that axis as "stretched", that is, the distances are perceived as larger.
In this way, each voter has their own perception of how important each issue is, and this is accounted for when computing the distance between different stances. This model of distance also naturally captures the correlations between multiple issues due to this scaling, and the effect of voters and candidates giving different, incompatible importance to issues. (A simple scaling factor wouldn't capture this, as it would be agnostic to the target voter/candidate, so there would be no degree of correlation due to opinion compatibility. But a scaling factor on top of the distributions would add an even greater degree of flexibility.)
With the Euclidean distance, and how we embedded the different priorities voters have on multiple issues in our model, we now have a unified model which can naturally deal with voters having strong ideals, degrees of compromising, etc. We could even model the dynamics of voters by using the notion of "effort to move around opinion units".
Note that there's still a distance between someone who is indifferent and anyone with an opinion. This makes sense, as it takes effort to convince someone to care. In polarizing situations, the indifferent voter and the undecided voter (the centrist) have similar but
The earth-mover's distance obeys many nice properties which preserve important features we want in this space of opinions, like a notion of partial orders which is required to rank compatibility across an issue in a consistent way, compatible with the overall geometric structure in multiple issues.
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