And while the median voter is a statistical construct and not a precisely identifiable figure, nevertheless we can see a politician do something and suppose that it preserves the structure of what the middle of their voters tend to vote for,
Nit: the optimum for a politician to target is often not the median/middle person who voted for them.
Consider a toy example: how much to spend on widgets. $0-$4,000. Every person has an opinion, uniformly distributed across the entire range. Assume that voters vote for the candidate who is closest to their target.
If you have two candidates, the optimums are not $1,000 and $3,000. It’s for one candidate to be $2,000-ϵ, and the other to be $2,000+ϵ.
Nit: the optimum for a politician to target is often not the median/middle person who voted for them.
Consider a toy example: how much to spend on widgets. $0-$4,000. Every person has an opinion, uniformly distributed across the entire range. Assume that voters vote for the candidate who is closest to their target.
If you have two candidates, the optimums are not $1,000 and $3,000. It’s for one candidate to be $2,000-ϵ, and the other to be $2,000+ϵ.