Tensions in Practice: The voting rule changes the winner¶
A committee choosing one proposal
The seven invented committee members rank three proposals as follows: three rank A before B before C; two rank B before C before A; two rank C before B before A. Plurality counts only first choices. Here a Borda rule gives two points for first, one for second and zero for third. The preferences stay fixed, yet the selected proposal changes. Neither result makes the losing members agree.
Honor first choices
Count the proposal each member most wants.
Use the whole ranking
Let lower-ranked preferences also influence the result.
Why these aims pull against each other
The two rules use different information from the same rankings. Broad second-place support can outweigh a larger first-place bloc under one rule and be ignored under the other.
Choose an arrangement to see what changes and what remains difficult.
Compare the same rows across alternatives. Cells state explicit toy quantities, membership or permissions; colors do not supply additional meaning.
What this choice protects
What it costs
When it fits
Compare the arrangements
Count first choices
Each member contributes one vote to their top proposal; the largest count wins.
| Count | Selected? | |
|---|---|---|
| A | 3 | Yes |
| B | 2 | No |
| C | 2 | No |
- What it protects
- Keeps the selection tied directly to first-choice support.
- What it costs
- Discards all second and third choices; the winner here has only three of seven first choices.
- When it fits
- Plausible when the committee explicitly values a plurality of first choices and accepts its limitations.
Illustration note: This is an editorial, deliberately bounded illustration. Its stated rules and any numbers are invented, not observations, recommended settings, or predictions.
Count rank points
Assign 2/1/0 points to first/second/third and add them across members.
| Count | Selected? | |
|---|---|---|
| A | 6 | No |
| B | 9 | Yes |
| C | 6 | No |
- What it protects
- Makes the broad support for B visible instead of discarding lower ranks.
- What it costs
- The point spacing is a rule choice; it lets B win with fewer first choices and is open to strategic reporting.
- When it fits
- Plausible when the committee has agreed in advance to value ranked compromise under this stated scoring rule.
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.
- These sincere rankings and rule definitions are fixed toy inputs. This comparison does not establish a universally fair rule or prove any impossibility theorem.
- Rank positions do not measure how strongly members care. The example does not analyze strategic equilibrium.
Source entries
Social Choice
Social choice T 1 supplies the local tension. The setting, alternative arrangements, and stipulated consequences are editorial applications.
Rule versus Outcome (the same preferences yield different collective answers)
The load-bearing insight is that the *rule*, not the preferences, manufactures the outcome — fix the profile and change the rule (plurality, Borda, Condorcet, IRV) and the winner changes.