Voting systems

Why voting methods matter

Most people assume that elections have a single “right” answer — that if we could just count the votes correctly, the will of the people would reveal itself. But this experiment demonstrates something far more unsettling: the counting method is itself a choice, and different methods encode different values. Plurality rewards passionate minorities. Borda count rewards broad acceptability. Ranked choice eliminates spoilers but can still produce paradoxes. The same ballots, the same preferences, the same voters — and yet the winner changes depending on which algorithm you feed them through. This is not a bug in democracy. It is a fundamental mathematical property of aggregating individual preferences into collective decisions.

Arrow’s impossibility theorem

In 1951, Kenneth Arrow proved what many political scientists had long suspected: no ranked voting system can simultaneously satisfy all reasonable fairness criteria. Specifically, Arrow showed that no system can satisfy all three of these: non-dictatorship (no single voter always determines the outcome), Pareto efficiency (if every voter prefers A to B, society should too), and independence of irrelevant alternatives (the choice between A and B should not depend on whether C is also running). Every ranked voting system must violate at least one of these axioms. This is not a failure of design — it is a theorem, as certain as the Pythagorean theorem. It means every voting system embodies a tradeoff, a decision about which kind of fairness to sacrifice. The question is never “which system is fair?” but rather “which kind of unfairness are we willing to accept?”

The Condorcet paradox

The Marquis de Condorcet discovered in 1785 that collective preferences can be cyclical even when every individual voter’s preferences are perfectly rational and transitive. If one third of voters prefer A over B over C, another third prefer B over C over A, and the final third prefer C over A over B, then a majority prefers A to B, a majority prefers B to C, and a majority prefers C to A. The group “prefers” in a circle. There is no Condorcet winner — no candidate who beats all others head-to-head. This is not a contrived edge case. It arises naturally whenever voters have diverse and cross-cutting preferences. Try the “Condorcet paradox” preset above to see it in action: rational individuals, irrational collective.

Strategic voting

The Gibbard-Satterthwaite theorem (1973) extends Arrow’s result in a devastating direction: every non-dictatorial voting system with three or more candidates is susceptible to strategic voting. That is, there will always be situations where a voter benefits by misrepresenting their true preferences. Under plurality, this manifests as the “lesser of two evils” phenomenon: supporters of a minor candidate vote for a major-party candidate to avoid “wasting” their vote. Under Borda count, voters may rank their second-favorite candidate last to give their favorite a better chance. Under IRV, voters may rank a strong competitor artificially low. No system is immune. The question becomes: which systems make strategic voting harder, riskier, or less rewarding?

Real-world implications

These are not academic curiosities. The 2000 U.S. presidential election — where Ralph Nader’s candidacy may have tipped Florida from Gore to Bush — is a textbook example of the spoiler effect under plurality voting. Alaska, Maine, and several other jurisdictions have adopted ranked choice voting specifically to mitigate this problem. France’s two-round system, Australia’s preferential voting, and New Zealand’s mixed-member proportional system all represent different answers to the same fundamental question Arrow identified. Each system produces different incentives for candidates, different strategies for voters, and different kinds of representation. The math guarantees there is no perfect answer — only informed tradeoffs.

Connection to collective intelligence

Social choice theory connects directly to the study of collective intelligence — the question of how groups aggregate information to make decisions. Joshua Becker’s research on social networks and belief formation shows that how people share and combine information shapes the quality of group judgments, sometimes improving accuracy and sometimes amplifying errors. Voting systems are aggregation mechanisms, and like any aggregation mechanism, they can be wise or foolish depending on their structure. The Condorcet jury theorem (1785) shows that majority voting can be remarkably accurate when voters have independent, better-than-random judgment. But change the aggregation rule — from majority to plurality to Borda — and you change which information gets amplified and which gets discarded. The design of the aggregation mechanism is itself an act of intelligence design. See also the network dynamics experiment, which explores how network structure shapes collective outcomes, and the Schelling segregation model, which demonstrates how individual preferences aggregate into collective patterns.