Median Voter Game, explained.
The median voter theorem explains why, under specific assumptions, the position preferred by the median voter can defeat other positions in majority comparisons.
Why it happens
On a single policy line with single-peaked preferences, moving away from the median leaves at least half of voters on the other side. In a simple two-candidate location game, competition can pull candidates toward the middle of the electorate.
When voters choose the nearer of two positions, location determines vote share.
Read the result
Move a candidate's position and compare vote shares under the stated voter preferences. The middle of this simulated distribution is an assumption; it need not match a real electorate's policy median.
A worked example
Choosing a meeting time
Five people prefer times at 9, 10, 11, 12, and 13, and each dislikes times more as they move away from their own ideal.
The median preference is 11. In a pairwise vote against an earlier or later time, at least three people prefer 11.
The result comes from the one-dimensional, single-peaked structure, not from every person preferring the same time.
OPTIONAL DEEPER DETAILGo deeper: inside the model
Inside this model
One hundred and one voters sit at integer positions 0–100 and choose the nearest of two platforms; exact ties split equally. The plot shows your vote share for every possible platform holding the rival fixed.
Where this idea is useful
A practical use
See why two competitors may cluster near the middle of a one-issue spectrum.
A common misconception
“Real elections must always be won by a centrist.”
Multiple issues, turnout, parties, unequal information, and non-single-peaked preferences can change the result. The theorem's assumptions matter.
What this explanation leaves out
- Actual voting has many dimensions, turnout differences, identity and more than two candidates.
Does median mean average?
No. The median splits ordered voters into two halves. An extreme preference can move the arithmetic mean without changing the median.
Can the relevant preferences be placed on one line with one preferred point each?
Associated thinkers
Further reading
Explore the original research or the teaching reference behind this experiment.