McKelvey’s theorem and facility choice

This post is a popularization of a (pretty well known) theorem by Richard McKelvey on agenda manipulation. This is a work of fiction, a fable, having nothing to do, whatsoever, with the real people or real events, whether in USD116 or outside of it.


In a quiet Midwestern town, a school district looks for a place to build, – let’s say, a swimming pool, to serve the kids of three schools located at points A, B and C.

A committee was duly formed to investigate possible options.

A nice option presented itself, at the location D. Everyone is fine with the location. However, the superintendent, who happens to live somewhat outside the district, near the point S, wants the pool next to their house (they really, really, really like a morning swim).

Who cares about what the superintendent likes, you’d think? Not so fast, responds the superintendent.

They set up three meetings of the committee crated “to evaluate various options, for the benefit of the whole district.”

At the first meeting, they offer the option E for consideration. Nothing especially wrong with D, they say, but isn’t E so much better?

The representatives from the school B objected, but the teams A and C preferred E over D: the pool would be closer to them. And so they voted to accept the proposal E.

On the next meeting, the superintendent told the Committee, that a different proposal emerged, at F. Now, the A folks liked it a lot. The representatives from C didn’t, and so it came to B to decide. The shrewd folks from B calculated that the option F will slightly improve their awful commute times compared to E, and voted for it. Thus F became the winning proposal after the second meeting.

At the third, and last meeting, the Superintendent (out of the blue) proposed to move the pool to S. The team B rejoiced: even closer to them! The gain of C was just tiny, but they were angry at A for their betrayal during the previous round, and so ignored their pleas and voted for the new position. So the future swimming pool location was assigned just next door to the Superintendent.

“Ah, the beauty of democracy” muttered the Superintendent closing the meeting.