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Voting methods

One of the most critical priority for any democracy is to improve its electoral system and start using a much better voting method.

  Casting and Tallying — The Two Phases of Every Election

Illustration

Every election, in every country, under every voting method, passes through two distinct phases.

The first phase is casting: what voters are asked to express. It concerns the design of the ballot and the question put to every voter when they enter the booth. What choices are available? How many can they select? How precisely can they express their preferences? This is the moment of democratic expression — and it is determined entirely by the ballot's design, before a single result is computed.

The second phase is tallying: how cast ballots are converted into an outcome. It is the mathematical operation that runs after polling closes — counting votes, aggregating scores, allocating seats, determining the winner. Tallying is constrained by what was expressed at casting: you cannot extract more information than the ballot allowed voters to provide.

These two phases are often treated as a single thing — "the voting system" — and the confusion between them is the single most common source of misunderstanding in debates about electoral reform. A reform that changes tallying only leaves the casting constraint untouched. A reform that changes casting changes what democratic expression is even possible.

Phase 1 — Casting: What the Voter Expresses

Casting is the moment of democratic expression. It happens in the privacy of the voting booth, before any counting begins. The ballot presents the voter with a set of candidates or options, and asks: what do you think?

The question sounds simple. Its design is not. Different ballot designs allow voters to express radically different amounts of information about their preferences:

Single-choice ballots

The most common design worldwide. The voter picks one candidate or one party. Everything else on the ballot remains blank. The voter may feel enthusiastic about their choice, or deeply reluctant — the ballot records neither. They may have opinions, positive and negative, about every other candidate — the ballot discards all of them. The instruction is simple: pick one.

Single-choice ballots are used under plurality voting (First-Past-The-Post), most forms of proportional representation (where the voter picks a party, not a candidate), and two-round systems (where a new single choice is made in each round). The consequences of this design — across every system that uses it — are documented in Single Choice Voting.

Ranked ballots

The voter orders candidates from most preferred to least preferred: 1st, 2nd, 3rd. This expresses more information than a single choice — the voter's ordering of candidates is recorded, not just their top pick. But it still does not capture intensity: whether a voter ranks Candidate A first by a wide margin or a narrow one is unknown. Ranked ballots are used in Instant Runoff Voting (IRV), the Single Transferable Vote (STV), and the family of Condorcet methods — which use the full ranking to find the candidate who beats every other candidate in head-to-head pairwise comparisons.

Approval ballots

The voter marks every candidate they consider acceptable. A voter can approve one candidate, or three, or all of them. This breaks the single-choice constraint: the ballot now captures the voter's opinion on every candidate simultaneously, not just their single favourite. The trade-off: it is binary — a candidate is either approved or not, with no degrees in between.

Score ballots

The voter assigns a numeric score to each candidate. This is the richest expression format: it captures intensity (strong support vs. grudging acceptance), covers every candidate, and allows the voter to express simultaneous preferences across the full field. Score Voting uses a positive-only scale (0 to 5). Informed Score Voting (ISV) uses a symmetric scale (−5 to +5), where the negative range serves a dual purpose: it expresses genuine opposition, and the floor value (−5) doubles as an explicit I Don't Know signal — asymmetric risk weighting built into the ballot design itself.

The casting design determines the ceiling of democratic expression. Whatever information is not captured at this stage cannot be recovered during tallying. A ranking cannot be reconstructed from a single X. A score cannot be reconstructed from a ranking. The ballot design is not a technical detail — it is the democratic question itself.

Phase 2 — Tallying: How Votes Become Results

Tallying is the mathematical operation that converts cast ballots into an outcome. It happens after polling closes, and it is entirely determined by the information that casting provided.

For a given set of cast ballots, different tallying rules can produce different results — a fact that has generated an entire field of social choice theory. But tallying cannot create information that was not expressed at casting. The mathematical operation is constrained by its input.

Plurality tallying

Count the votes for each candidate. The candidate with the most votes wins. Simple, fast, and familiar — but it treats a 40% plurality the same as a 90% landslide, and it discards every preference below the winner's threshold.

Proportional tallying

Seat allocation is distributed in proportion to each party's share of the total vote. Parties that receive 30% of the vote receive approximately 30% of the seats. This changes the tallying method substantially — but if the casting design is single-choice (pick one party), the information entering the tally is still limited to one expression per voter.

Sequential elimination (IRV / STV)

In ranked systems, if no candidate achieves a threshold in the first count, the lowest-ranked candidates are eliminated and their voters' second preferences are redistributed. This is a more complex tallying operation — multiple rounds of counting run on the same set of ballots. It extracts additional information from ranked ballots that single-choice tallying would discard. But it still cannot extract what was not expressed: intensity, simultaneous approval across multiple candidates, or scores.

Pairwise comparison (Condorcet)

In Condorcet methods, ranked ballots are used to run a virtual head-to-head contest between every pair of candidates. If Candidate A is ranked above Candidate B by a majority of voters, A "beats" B. The Condorcet winner is the candidate who beats every other candidate in these pairwise contests — and is widely considered the most democratically legitimate outcome when one exists. The difficulty arises when no such winner exists: cycles can form (A beats B, B beats C, C beats A), and resolving them requires a disambiguation algorithm. Experts disagree about which algorithm is correct — a problem with deep consequences for democratic legitimacy.

Score aggregation

In scored systems, each candidate's scores are summed (or averaged) across all voters. The candidate with the highest aggregate score wins a seat, and the process continues until all seats are filled. This tallying method requires scored ballots to function — it has no meaningful operation on single-choice input. The richness of the result matches the richness of the expression.

These tallying methods are not interchangeable substitutes. Each requires a corresponding casting design to be meaningful. The tallying method chosen must match — and honour — the information that casting collected.

Why the Distinction Matters — and Is Routinely Missed

In public debates about electoral reform, casting and tallying are almost universally conflated. The consequences are significant.

Reforms that change tallying only

Proportional representation changes how seats are allocated (tallying) but preserves the single-choice ballot (casting). The voter still picks one party. The pathologies that flow from that single-choice constraint — the pressure to vote strategically, the blurring of individual candidate accountability behind party lists, the inability to express simultaneous preferences — are unaddressed. Proportional tallying distributes the outcome more equitably among parties. It does not expand what individual voters could express.

Instant Runoff Voting (IRV) adds preference ranking to the ballot — a partial casting improvement — but the ranked design still does not capture intensity or simultaneous approval. And IRV's sequential elimination tallying introduces its own distortions: results can change depending on elimination order, and a candidate who wins more first-preference votes may lose to a candidate who wins more second-preference redistributions. The reform is real but incomplete, and the IRV tallying algorithm has been criticised for producing non-monotonic outcomes — where giving a candidate a higher ranking can cause them to lose.

Reforms that change casting

Approval Voting and Score Voting change the casting design fundamentally: voters are no longer restricted to a single choice. This changes what democratic expression is possible — and the tallying method must change to match. The two phases must be redesigned together. The casting change is the more significant of the two: once voters can express more, the tallying question becomes how best to honour that expression, which is a tractable mathematical problem. Expanding expression is the structural reform; tallying is its instrument.

The practical significance: many proposals celebrated as "electoral reform" are tallying-only reforms. They produce different outcomes from the same limited expression. The more fundamental question — what should voters be allowed to express? — is left unanswered.

Technology — Integrity at Both Stages

The casting/tallying distinction maps directly onto the most consequential debates about voting technology — and helps clarify what is at stake at each stage.

Casting integrity

The voting booth must ensure that each voter's expressed preference is captured accurately and privately. The risks at this stage are: the voter making an error they did not intend, the ballot design confusing or misleading voters, and the voting interface compromising the secrecy of the ballot. For complex ballots — such as scoring 15 or 20 candidates on a 0–5 scale — a well-designed ballot-marking device can help the voter review their choices before finalising them, reducing inadvertent errors. The critical constraint: the marking device assists the voter; it does not record the vote. Its output is a printed ballot that the voter reviews and carries to the ballot box personally.

Tallying integrity

After polling closes, the question is whether the tally accurately reflects what was cast. The risks are miscounting, tampering, and — critically — a counting process that cannot be independently verified. For complex scored ballots, an optical scanner that reads each physical ballot and computes aggregate scores provides a fast, accurate initial tally. The physical paper ballots are preserved throughout as the authoritative legal record. When the scanner's casing is transparent — so that each ballot is visible as it travels through the machine — citizens present in the room can observe the count in continuous, unbroken view.

But the initial tally is not the end of tallying integrity. A tally that can be independently verified is a fundamentally different democratic instrument from a tally that must simply be trusted. The paper record makes such verification possible: the machine's count can be checked against the physical ballots by hand, stack by stack, under public observation. The deeper questions — how much of the tally must be verified to certify a result with confidence, who controls the selection of ballots for checking, whether ordinary citizens present in the room can play a direct role in that selection, and whether post-election verification is a standard democratic instrument applied after every election or a remedy reserved for disputed results — define what election integrity actually means, beyond the mechanics of the initial count. These questions are addressed in the Pildem tallying and audit framework, which accompanies this architecture.

The architecture principle

The Pildem Framework's position on voting technology reflects the casting/tallying distinction directly: machines assist, paper decides. The three functions of election technology are kept strictly separate:

Function Tool Chain of custody
Casting assistance — helps the voter express their choices correctly Ballot-marking device (in booth, offline, open source) Voter-controlled; output is printed paper
The legal ballot — the authoritative record of the vote Physical paper, printed by the device and reviewed by the voter Voter carries it to the ballot box personally
Tallying assistance — counts the physical ballots Optical scanner (open source, publicly observable) Paper preserved as authoritative record; machine tally independently verifiable by physical audit

The casting machine and the tallying machine are different physical devices with different functions. Neither is the ballot. The paper is always the ballot. Digital conspiracy requires only a vulnerability; physical conspiracy requires physically altering thousands of individual pieces of paper under public observation — a structurally different and far more detectable proposition.

Open-source software and hardware specifications for both devices ensure that citizens, security researchers, and electoral observers can audit the tools that assist their democracy — not merely trust proprietary systems whose inner workings are invisible. The same openness that governs the tools should govern the process: an election whose machines are transparent but whose tally is closed to citizen verification has achieved transparency of method without transparency of result.

Casting and Tallying Across Voting Methods

The following table shows how each major voting method handles the two phases. The diversity of tallying methods is visible and familiar; the relative uniformity of casting design — most systems restrict voters to a single choice or a ranking — is the less-discussed pattern.

Voting method Casting design Tallying method
Plurality (FPTP) Single choice: pick one candidate Most votes wins (plurality)
Proportional representation (party list) Single choice: pick one party Seats allocated proportionally to party vote share
Two-round (runoff) Single choice per round; two rounds Top two advance; majority in round 2
Instant Runoff (IRV / RCV) Ranked order of preference Sequential elimination; lower preferences redistributed
Single Transferable Vote (STV) Ranked order of preference Proportional via quota and transfer of surplus
Condorcet methods (Schulze, Ranked Pairs, etc.) Ranked order of preference Pairwise comparison; Condorcet winner if one exists; disambiguation algorithm if cycles occur
Approval Voting Binary per candidate: approve or not (as many as desired) Most approvals wins
Score Voting Numeric score per candidate (e.g. 0–5) Highest total or average score wins
Informed Score Voting (ISV) Numeric score per candidate (−5 to +5) + I Don't Know option (scored as −5) Score aggregation; IDK scored as −5 (asymmetric risk weighting)

The first five methods in this table share a casting design that restricts the voter to a single choice or a single ordering of choices. The final three break this restriction — and all three require a corresponding change in tallying method to honour the richer expression. The casting change is the more fundamental of the two reforms. Tallying, once the expression is available, is mathematics.

A Third Question — Who Appears on the Ballot?

The casting/tallying distinction covers everything that happens from the moment the voter enters the booth to the moment a result is declared. But before the first vote is cast, a prior question has already been answered: who is on the ballot?

Ballot access — the mechanism by which candidates earn the right to stand — is the upstream condition that determines the field of democratic choice. A casting design that allows voters to score every candidate on a richly expressive scale is only as good as the candidates it presents. If the field is filtered by party machines, financial barriers, or administrative hurdles that favour incumbents over genuine challengers, the expressiveness of the ballot cannot compensate for the poverty of the choice.

Different democracies resolve ballot access in radically different ways: signature requirements ranging from ten to hundreds of thousands, monetary deposits, endorsement by elected officials, prior electoral performance thresholds. The range of mechanisms is wide; the principles for evaluating them are contested. One principle stands out as consistent with the logic of scored voting: if a candidate's public standing can be measured by how voters who know them actually score them, then that score — accumulated across prior electoral cycles — is democratic evidence that no deposit amount or signature count can replicate. The logic of the scored ballot extends naturally upstream, from how votes are counted to who earns the right to be counted.

How casting design and ballot access interact — and how a scored ballot system opens the door to a fundamentally different approach to candidate eligibility, rooted in demonstrated public support rather than institutional gatekeeping — is addressed in the Informed Ballot Access Protocol.

Voting methods

One of the most critical priority for any democracy is to improve its electoral system and start using a much better voting method.

Single Choice Voting

First Past the Post, Proportional Representation, two-round runoffs — political scientists treat these as fundamentally different systems. From the voter's side of the ballot, they all issue the same instruction: pick one. That shared constraint is the root of the Duverger Syndrome.

Instant Runoff Voting

Instant Runoff Voting is not the improvement that its advocates claim. It does not fully eliminate the spoiler effect; it produces paradoxical results that violate basic fairness intuitions, and it cannot be counted precinct by precinct. IRV is a detour, not a destination.

Informed Score Voting: Elevating Knowledge, Empowering Choice

Frustrated with uninformed voters and endless candidate lists? Informed Score Voting empowers you to express what you do know while acknowledging what you don't, leading to more thoughtful elections and better representation.

Approval Voting: A Simple Path to Stronger Democracies

Tired of choosing the "lesser of two evils"? Approval Voting offers a refreshingly simple way to empower voters and elect candidates who truly represent their values. This powerful alternative can strengthen our democracies.

Score voting: Rate, Don't Just Pick

Tired of feeling limited by "choose-one" voting? Score Voting empowers you to rate candidates on a scale, expressing the strength of your support and helping elect leaders who truly represent your values.

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