The Best Way to Elect

Three Ways to Count a Ranked Ballot A simulation study comparing three ranked choice voting systems using a mayoral election in the fictional Town of Westbrook — 10,000 voters, 6 candidates, same ballots, three different outcomes. --- The Question Ranked choice voting is not a single system. It is a family of systems distinguished by one deceptively simple question: after a candidate is eliminated, what happens to the votes? The answer determines who wins. It shapes which coalitions matter, how much a second preference is worth, and whether a candidate with narrow but passionate support can beat one with broad but lukewarm appeal. To explore these differences concretely, we simulated a six-candidate mayoral election in the Town of Westbrook with 10,000 voters, each casting a fully ranked ballot. We then counted those ballots three different ways — arriving, through iteration and critique, at what we believe is the most defensible system of the three. The Setup Six candidates are running for mayor of Westbrook: John — a steady incumbent with loyal but not overwhelming support Robert — a pragmatist with strong second-preference appeal Alfred — a reform candidate with an energised base Raymond — a long-shot with a small but fervent coalition Sebastian — a centrist liked by many, loved by few Isidra — a frontrunner with strong first-choice numbers and broad secondary appeal Voters were distributed across seven preference coalitions, weighted to reflect realistic bloc voting patterns. Each ballot ranks all six candidates. A small random shuffle was applied to a subset of ballots to simulate real-world variation in how voters express their preferences. The same 10,000 ballots were then fed into three different counting systems. Same voters. Same preferences. Different rules.

Scenario 1: Cumulative Ranking — All Ballots, Every Round The first system takes a maximally inclusive approach. In each round, every ballot contributes its preferences up to that rank level, cumulatively. Round 1: Count everyone's rank-1 pick. Eliminate the candidate with the fewest. Round 2: Count rank-1 and rank-2 picks from all 10,000 ballots. Add them together. Eliminate the new lowest. Round 3: Count ranks 1, 2, and 3 from all ballots. Eliminate the new lowest. Continue until one candidate remains. The logic is intuitive: the deeper into the ranking you go, the more complete a picture of the electorate's preferences you have. By round 5, every single preference on every ballot has been counted. What the simulation showed: Round 1: Sebastian eliminated (975 votes). John leads with 2,524. Round 2: Raymond eliminated (2,877). John still leads with 4,804. Round 3: Robert eliminated (2,938). John extends his lead to 7,728. Round 4: Isidra eliminated (7,131). Alfred closes the gap — John 9,015, Alfred 8,713. Round 5: Alfred overtakes John at the final rank level, winning 9,977 to 9,967. Winner: Alfred — by just 10 votes. The problem with Scenario 1: Notice those totals. By round 5, the candidates together have accumulated nearly 20,000 votes from 10,000 voters. That is because every ballot contributes at every rank level, even in rounds where a voter's first-choice candidate is still in the race. A voter who ranked Alfred first is also boosting the rank-2 tally in round 2, even though Alfred hasn't been eliminated yet. This is a form of double-counting — your influence is being tallied multiple times in a single election. The numbers become impossible to explain to voters. A system that produces totals of 9,977 from an electorate of 10,000 is hard to defend at a town hall. And Alfred's paper-thin margin of 10 votes is an artifact of this inflation, not a meaningful signal from the electorate.

Scenario 2: Targeted Redistribution — The Loser's Ballots, Fixed Rank Scenario 2 corrects the double-counting problem by limiting redistribution: only the eliminated candidate's own rank-1 supporters' ballots move, and only at the rank position corresponding to the current round. Round 1: Count everyone's rank-1 pick. Eliminate the lowest. Carry those counts forward. Round 2: Look only at the just-eliminated candidate's rank-1 supporters. Count their rank-2 picks. Add those to the running totals. Eliminate the new lowest. Round 3: From the new loser's rank-1 supporters, count their rank-3 picks. Add and eliminate. Continue until one candidate remains. Vote totals grow slowly and stay within an interpretable range. No ballot is counted more than once per round. Only the votes of eliminated candidates move. What the simulation showed: Round 1: Sebastian eliminated (975 votes). Round 2: Sebastian's 975 supporters' rank-2 picks are redistributed. Raymond eliminated at 1,252. Round 3: Raymond's supporters' rank-3 picks added. Robert eliminated at 1,683. Round 4: Robert's supporters' rank-4 picks added — Alfred jumps to 3,873. Isidra eliminated at 2,316. Round 5: Alfred wins 3,873 to John's 2,578. Winner: Alfred — this time by a clear margin. The problem with Scenario 2: The fixed rank position creates a quiet but serious flaw. In round 2, we look at rank-2 on the eliminated candidate's ballots. But what if a voter's rank-2 pick was also eliminated in round 1 — before we even checked? That ballot contributes nothing to round 2, not because the voter had no further preferences, but because the system failed to look for them. The problem compounds as the rounds go on. By round 4, we are looking at rank-4 picks on the eliminated candidate's ballots. But that voter's rank-2 and rank-3 picks may have already been eliminated in previous rounds. A ballot that could have meaningfully contributed simply vanishes — silently, without the voter ever knowing.

Scenario 3: Classic Instant-Runoff Voting — Next Available Candidate The third scenario resolves both problems. It keeps the core principle of Scenario 2 — only the eliminated candidate's votes move — but fixes the rigid rank-position problem by letting each ballot find its next available candidate, no matter what position that falls in. Every ballot is "owned" by whichever active candidate is ranked highest on it — their first choice. Each round, tally the live ballot owners. The candidate with the fewest owned ballots is eliminated. Every ballot owned by the loser walks down that voter's preference list and finds the next candidate still in the race — skipping anyone already eliminated. Repeat until one candidate holds a majority of active ballots. This is classical Instant-Runoff Voting (IRV), used in Australia, Ireland, Maine, Alaska, and New York City. What the simulation showed: Round 1: Sebastian eliminated (975 votes). John leads with 2,524. Round 2: Sebastian's ballots redistribute to each voter's next available pick. Raymond eliminated at 1,252. Round 3: Raymond's ballots redistribute. Isidra is now eliminated at 2,276, behind Robert (2,909), John (2,524), and Alfred (2,291). Round 4: Isidra's ballots flow to each voter's next available preference. Alfred eliminated at 2,352. John now leads with 4,739. Round 5: Alfred's ballots redistribute — John wins 7,029 to Robert's 2,971. Winner: John — a majority of active ballots, and a different winner than either previous scenario. Why this is better: No double-counting. Each ballot is owned by exactly one candidate at any point. Vote totals always equal the number of active, non-exhausted ballots. The numbers never exceed 10,000. No wasted votes due to fixed rank positions. A ballot doesn't care which round it's in. It simply asks: who is the highest-ranked person on my list who is still running? That candidate gets the vote. Transparent and auditable. At any round, you can see exactly which ballots moved, where they went, and why. The redistribution is traceable ballot by ballot. The one honest caveat: if a voter only ranked their top two or three candidates and all of those get eliminated, their ballot becomes exhausted and contributes nothing to the final rounds. This is a real limitation — but it applies to any redistribution system. The difference is that IRV makes exhaustion visible and honest, rather than obscuring it behind inflated totals or fixed rank positions.

What the Three Scenarios Produced Here is the full elimination order across all three scenarios: Scenario 1 Scenario 2 Scenario 3 Round 1: Sebastian Sebastian Sebastian Round 2: Raymond Raymond Raymond Round 3: Robert Robert Isidra Round 4: Isidra Isidra Alfred Round 5: John John Robert Winner: Alfred Alfred John The first two rounds are identical across all three systems — Sebastian and Raymond are eliminated regardless of counting method, because their first-choice support is low enough that no redistribution scheme saves them. The scenarios diverge at round 3. In Scenarios 1 and 2, Robert is eliminated next. In Scenario 3, Isidra falls instead — because under pure live-ballot counting, Robert has accumulated more redirected ballots than Isidra at that point. This divergence cascades: the order in which candidates exit changes who absorbs their supporters, which changes the final standings entirely. Scenarios 1 and 2 both elect Alfred. Scenario 3 elects John. These are not the same outcome dressed differently. They reflect genuinely different interpretations of what the voters said. The Deeper Point When all three methods agree on a winner, that candidate is hard to dispute — they won under every reasonable interpretation of the ballots. When the methods disagree, as they do here, the choice of counting system is no longer a technical footnote. It is a political decision about what elections are actually measuring. Scenario 1 says: the winner is whoever accumulates the most preference-weight across all voters and all rank levels. Alfred wins because he is consistently ranked near the top by a large share of the electorate, even if he is not anyone's runaway first choice. Scenario 3 says: the winner is whoever most voters would rather have than the alternative when it comes down to a choice. John wins because when the field narrows, enough voters' redirected preferences land on him — he is the candidate who survives head-to-head attrition. Neither answer is wrong. They are answers to different questions. What makes Scenario 3 the most defensible is not that John is obviously the correct winner — it is that the system itself is the most honest. No vote is counted more than once. No vote is silently discarded because its rank position happened to be already eliminated. The vote totals at every round mean what they appear to mean. And the winner can be said, without qualification, to hold majority support among the voters whose preferences could be expressed under the rules. Conclusion We began by asking what happens to votes after an elimination, and found that the answer has real consequences — including, in this simulation, producing three different winners depending on which method you use. Scenario 1 is interesting as a thought experiment but unfit for real elections. It counts ballots multiple times and produces totals that exceed the size of the electorate. Scenario 2 is a genuine improvement — targeted, slow-growing totals, no double-counting — but it silently discards votes when a ballot's fixed rank position has already been eliminated. Scenario 3, classic IRV, resolves both issues. Every displaced ballot finds a home. Vote totals remain meaningful. The winner earns majority support from the active electorate. It is the only system of the three that is both fair to voters and honest about what the result means. The journey from Scenario 1 to Scenario 3 is the journey from an intuitive but flawed idea toward a principled and battle-tested one. The destination is not perfect — no electoral system is — but it is honest, and in democratic design, honesty about how votes are counted is not a minor virtue. Notes: Simulation details: 10,000 voters, 6 candidates, 7 preference coalitions, seeded random number generator for reproducibility. All three scenarios used identical ballots.