The median voter's location depends entirely on how voters are distributed across the ideological spectrum. Explore how different distributions shift the median and what that means for party competition.
The distribution matters. In the Downsian model, both parties converge to the median voter - not the mean. The median's location depends on the shape of the distribution. Select a preset to see how the distribution changes the median and what that implies for party competition.
Distribution presets
0
Median voter
0
Mean voter
0
Mean minus Median
Key implications
Median is not Mean
In a skewed distribution the mean and median diverge. Parties should converge to the median - the point that wins a majority vote - not the average position.
Who turns out matters
Voter turnout and registration rules shift the effective median. If one wing votes at higher rates, the median moves toward it and parties follow.
Demographics shift medians
As electorates age, urbanise, or change, the distribution shifts. Both parties must track the new median even if their core voters have not changed.
Bimodal distributions
Even with two voter peaks, the mathematical median is still one point. Both parties converge there in theory - but both abandon their base, which creates credibility problems.
Shape the electorate. Use the sliders to design a voter distribution. Control where voters cluster, how spread out they are, and how skewed the distribution is. Watch how the median and mean respond.
Distribution parameters
0
18
0.0
0%
0
Median voter
0
Mean voter
0
Mean minus Median
Follow the median. Choose a distribution, then drag Party A and Party B to compete. The median line is fixed by the distribution. Place both parties on the median to confirm it is the Nash equilibrium.
Drag Party A and Party B. The median is fixed by the distribution above.