Tensions in Practice: A compromise ballot can change the winner¶
Six voters using the same plurality rule
Six fictional voters choose among A, B and C. Two rank A first, two B first and two C first. One of the B-first voters, V, ranks B above A above C; everyone else’s ballot is held fixed. Highest ballot count wins, with ties broken C before A before B. If V votes B, the three-way tie elects C. If V instead votes A, A wins 3–1–2. V’s true ranking and the voting rule have not changed.
Record first-choice support
Cast the ballot for the option the voter genuinely ranks first.
Seek a preferred achievable result
Use the ballot to obtain a better outcome than sincere voting yields under the declared others’ ballots.
Why these aims pull against each other
A plurality ballot is both a report of support and an instrument that changes the outcome. In this fixed profile, using it for the latter purpose suppresses a first-choice count even though that preference remains.
Choose an arrangement to see what changes and what remains difficult.
True first counts genuine first preferences; Ballots counts submitted votes. Only voter V changes a ballot, from B to A. Highest count wins; the declared tie priority is C, then A, then B.
What this choice protects
What it costs
When it fits
Compare the arrangements
Vote the first choice
V votes B, producing counts 2, 2 and 2. The announced tie rule selects C, V’s last-ranked outcome.
| True first | Ballots | Wins | |
|---|---|---|---|
| A | 2 | 2 | No |
| B | 2 | 2 | No |
| C | 2 | 2 | Yes |
- What it protects
- The ballot and tally faithfully retain V’s first-choice support for B.
- What it costs
- Given the fixed other ballots and tie rule, the elected outcome is worse for V than the outcome available through the compromise ballot.
- When it fits
- Plausible when sincere expression or a commitment to honest first-choice reporting is itself an important aim; this is not the outcome-maximizing action in the stated profile.
Illustration note: This is an editorial, deliberately bounded illustration. Its stated rules and any numbers are invented, not observations, recommended settings, or predictions.
Vote the compromise
V votes A. The tally becomes A 3, B 1, C 2 and A wins, which V prefers to C while still preferring B to A.
| True first | Ballots | Wins | |
|---|---|---|---|
| A | 2 | 3 | Yes |
| B | 2 | 1 | No |
| C | 2 | 2 | No |
- What it protects
- V obtains the better of these two achievable elected outcomes under the stipulated complete information.
- What it costs
- The ballot no longer records V’s first choice; reading the tally as the true first-choice distribution would overstate A and understate B.
- When it fits
- Plausible when V prioritizes the elected result and has reliable knowledge of the fixed other ballots; uncertainty or changed ballots can defeat the calculation.
Illustration note: This is an editorial, deliberately bounded illustration. Its stated rules and any numbers are invented, not observations, recommended settings, or predictions.
What this illustration does—and does not—establish
The source establishes the structural tension; the concrete alternatives and their conditional costs are editorial synthesis. No arrangement is a universal recommendation.
- The profile and tie order are invented. The example is not a recommendation about a real election and predicts no actual voting behavior.
- Only V’s report changes. Both A-first voters can be taken to rank A > B > C, the other B-first voter B > A > C, and both C-first voters C > A > B; their lower ranks do not enter this tally.
- The sincere arrangement serves an expressive or reporting aim, not a claim that it maximizes V’s outcome ranking. This single counterexample establishes a manipulation opportunity for this rule/profile, not an impossibility theorem for every voting system.
Source entries
Social Choice
Social choice Sincere versus Strategic Input (the strategyproofness gap) supplies the local tension. The setting, alternative arrangements, and stipulated consequences are editorial applications.
Sincere versus Strategic Input (the strategyproofness gap)
The failure mode is treating reported preferences as sincere when the rule rewards strategic voting, so the outcome aggregates manipulation rather than values.