The "political spectrum" is often expanded from a one dimensional scale from left to right to a two dimensional system on axes such as social policy or fiscal policy. Whatever the axes it is a useful metaphore.
Below are simulations of elections based on putting voters and candidates in a two dimensional space of political thinking. Candidates take various positions and voters tend to vote for the closest candidates. The graphs are made by simulating a voting populace centered at each point in the image. Diversity in the voters is over a gaussian distribution around that center. This randomness causes some fuzz in the graphs in regions where an election method is sensitive enough to that noise to occasionaly flip the result.
The simulations were all run on a plane from -1.0 to 1.0 in the x and y axes. The population gaussian had a sigma of 1.0 . For a distance 'r' from a voter to a candidate, the voter's utility for that candidate is 1/r. 4 elections with 10000 voters were averaged to find the color of each pixel, mixing the colors of the winning candidates when not all elections go the same way. The position of each candidate is represented by a diamond with the color representing that candidate.
These three candidates are at the edges, 1,1 -1,1 0,-1
| Max Social Utility | Pick One |
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| IRV | IRNR |
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| Condorcet | Rating Summation |
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| Borda | Approval (Zero Info Strategy) |
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| Vote For And Against | Approval (With Poll) |
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These four candidates are at the corners, 1,1 -1,1 -1,-1 1,-1
| Max Social Utility | Pick One |
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| IRV | IRNR |
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| Condorcet | Rating Summation |
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| Borda | Approval (Zero Info Strategy) |
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| Vote For And Against | Approval (With Poll) |
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Three choices at -0.86,-0.66 -0.02,-0.98 -0.18,-0.96
| Max Social Utility | Pick One |
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| IRV | IRNR |
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| Condorcet | Rating Summation |
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| Borda | Approval (Zero Info Strategy) |
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| Vote For And Against | Approval (With Poll) |
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Three choices at 0.86,-0.02 0.58,-0.16 -0.46,-0.10
| Max Social Utility | Pick One |
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| IRV | IRNR |
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| Condorcet | Rating Summation |
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| Borda | Approval (Zero Info Strategy) |
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| Vote For And Against | Approval (With Poll) |
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Three choices at 0.08,-0.06 0.54,0.28 -0.74,-0.80
| Max Social Utility | Pick One |
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| IRV | IRNR |
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| Condorcet | Rating Summation |
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| Borda | Approval (Zero Info Strategy) |
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| Vote For And Against | Approval (With Poll) |
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Four choices at -0.76,-0.44 0.70,0.40 -0.22,-0.44 0.94,-0.72
| Max Social Utility | Pick One |
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| IRV | IRNR |
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| Condorcet | Rating Summation |
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| Borda | Approval (Zero Info Strategy) |
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| Vote For And Against | Approval (With Poll) |
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Four choices at -0.52,-0.54 -0.62,0.24 -0.92,0.28 0.70,0.10
| Max Social Utility | Pick One |
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| IRV | IRNR |
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| Condorcet | Rating Summation |
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| Borda | Approval (Zero Info Strategy) |
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| Vote For And Against | Approval (With Poll) |
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Four choices at -0.20,0.14 -0.68,0.08 -0.90,0.24 0.82,0.40
| Max Social Utility | Pick One |
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| IRV | IRNR |
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| Condorcet | Rating Summation |
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| Borda | Approval (Zero Info Strategy) |
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| Vote For And Against | Approval (With Poll) |
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