User:Psephomancy/2D election simulation examples

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2D election example with vote splitting and spoiler effect.png

This is an example simulation of an election on a 2-dimensional political spectrum (such as the Political Compass, Nolan chart, Pournelle chart, etc.; it doesn't matter what the actual axes are.)

There are 3000 voters (black dots), 3 candidates (colored dots), and voters vote honestly, supporting the candidates who are most similar to them ideologically (nearest distance).

  • C is a partisan candidate on the right
  • A is another partisan candidate, this time on the left
  • B is a moderate candidate, and the best representative of the average voter

FPTP[edit | edit source]

C wins under first-past-the-post voting, since A and B split the votes of the left wing of the electorate. (If A hadn't run, then B would have won. If B hadn't run, then A would have won. But since they both ran in the same election, C won instead.)

2D election example A vs B vs C.png

IRV[edit | edit source]

A wins under Instant-Runoff Voting ("Ranked-Choice Voting"), after B is eliminated for not having enough first-preference votes, leaving A and C. (A is slightly closer to the center, so more people in the center support A over C.)

First round is the same as plurality:

2D election example A vs B vs C.png


Second round after B is eliminated:

2D election example A vs C.png

Top-two runoff / Open primary[edit | edit source]

A wins under top-two runoff or an open primary. A and C have the most votes and proceed to the runoff. (None of the candidates gets over 50% in the first round.) A is slightly closer to the center, so more people in the center support A over C in the runoff.

First round is the same as plurality:

2D election example A vs B vs C.png


Second round after B is eliminated:

2D election example A vs C.png

Score[edit | edit source]

2D election example Scores for A, B, C.png

B wins under Score Voting (with normalized ballots), as they are the highest-rated overall by the voters. (Dark-colored voters gave that candidate a maximum score, white-colored voters gave them a minimum score.)

Condorcet[edit | edit source]

B also wins under Condorcet methods, as B would beat both A and C in head-to-head elections.

A vs B:

2D election example A vs B.png


B vs C:

2D election example B vs C.png

STAR[edit | edit source]

B also wins under STAR Voting. The first round is the same as Score, so the top-two winners are A and B (since A is slightly closer to the center than C):

2D election example Scores for A, B, C.png

B is then preferred over A by a 66% majority.

2D election example A vs B.png