In my Cost/Benefit Analysis course, I teach one segment on Public Choice. One of the issues I get into is the median voter theorem. I point out that it applies more directly to direct democracy, i.e., voting on initiatives and referenda, than to representative democracy, i.e., voting on candidates. The reason is that on the latter, people typically vote for a candidate who takes positions on more than one issue, usually many more.
But I have a problem. I'll quote from the text I'm using, Harvey S. Rosen's and Ted Gayer's Public Finance. The book gives the example of Donald, Daisy, Huey, Dewey, and Louie voting on how much money to spend on a party. Their preferred expenditures are: $5, $100, $150, $160, and $700. So the median voter is Huey and so if the outcome reflects the preference of the median voter, it will be $150. Here's what the text says:
A movement from zero party expenditure to $5 would be preferred to no money by all voters. A movement from $5 to $100 would be approved by Daisy, Huey, Dewey, and Louie, and from $100 to $150 by Huey, Dewey, and Louie. Any increase beyond $150, however, would be blocked by at least three voters: Donald, Daisy, and Huey. Hence the majority votes for $150.
HERE'S WHAT I DON'T GET:
Who is deciding what gets voted on? If someone decides that we're voting between spending $5 and spending $160, then $150 CAN'T emerge as the outcome. Indeed, what is the actual experiment that Rosen and Gayer are running? Are they going pairwise, from $0 to $5, and then $5 to $100, and then $100 to $150, etc.? It sounds like it. But have you ever heard of a vote like that?
I can see that if representatives are running and there's only one issue they'll decide, there's a tendency for them to choose to run at or close to the median voter's preference. But, typically, representatives will vote on many issues--that's why they're representatives. So if the median voter theorem means anything, it should apply to referenda and initiatives.