Temporal Proportional Representation: Vote Refunds Over Time for Fair Elections

Temporal Proportional Representation (PR), proposed by thomascolthurst on LessWrong, offers a novel way to achieve proportional outcomes for single-seat offices like the presidency without redrawing districts. In traditional PR, seats are allocated proportionally to vote shares. Temporal PR extends this concept over time: if party A consistently gets 60% of the vote, it should win the office 60% of the time. A simple method is letting a random voter decide each election, but that can produce unfair streaks (e.g., 12.5% chance of four consecutive wins for evenly matched parties).

The 'Wasted Vote Refund' system is a more sophisticated variant with provably minimal variance. In this scheme, each voter receives a vote every election, which remains valid until their chosen candidate wins. When a candidate wins, they must collectively pay N votes (total voters). If they have fewer than N votes (including stored ones), they borrow the shortfall from the losing voters, granting the losers extra votes in the next election. For example, with two parties of 50 members each, a random tie-break leads to Party A winning. Party A borrows 50 votes from Party B, leaving A with 0 and B with 2 votes each. Next election, Party B wins easily, pays back, and both parties reset to 1 vote each. The cycle repeats, ensuring long-term 50-50 balance. The theorem proves that in a static population with constant party support, the system elects each party proportionally over time, minimizing variability and encouraging voter participation.