Voting System Strategist

Example 1: Diagnosing a Condorcet Cycle (Committee Vote)

Setup: A product committee of 12 must choose between Feature A (performance), Feature B (usability), Feature C (integration). Preference profile:

          Engineering (5)   Design (4)   Business (3)
1st           A                B             C
2nd           B                C             A
3rd           C                A             B

Pairwise check:

Result: B beats A and C. No cycle. B is the Condorcet winner — the option that would win any head-to-head vote. Recommend Feature B regardless of voting system.

Example 2: Agenda Control in a Board Vote

Setup: A board of 7 must choose among Status Quo (S), Proposal A, and Proposal B. The board chair can set the vote order. Preference cycle: A beats S, S beats B, B beats A.

Backward induction by agenda:

Diagnosis: The chair can produce any of the three outcomes by choosing the agenda. If the chair prefers A, use Agenda 3. If the chair prefers B, use Agenda 2.

Countermeasure: If you are not the agenda-setter and you see a cycle, identify which option the agenda is designed to produce by tracing backward induction on the proposed vote order. If it does not serve you, propose a different vote order — or propose a voting system change (Condorcet pairwise) that eliminates agenda sensitivity.

Example 3: Strategic Voting Decision

Setup: A primary election with three candidates: your preferred candidate X (progressive, 15% polling), candidate Y (moderate, 45%), and candidate Z (conservative, 40%). You prefer X > Y > Z.

Analysis:

Why sincere voting hurts you: Voting for X means your vote does not participate in the Y vs. Z decision. If Y loses to Z by a small margin, your sincere vote contributed to your worst outcome.

The paradox stated plainly: It is only okay to vote sincerely (for X) when the election is not close — when your vote will not matter anyway. The moment your vote matters, strategic voting for your best viable option is the rational choice.

Example 4: Choosing a Voting System for an Organization

Setup: A professional society with 200 members needs to elect 3 people to an advisory board from 12 nominees. Currently uses plurality with each voter casting 3 votes.

Problem diagnosis: With 12 candidates and 3 votes each, coordinated blocs can dominate — a minority with focused votes can sweep all three seats. The Joe DiMaggio effect: the obvious strongest candidate gets abandoned by strategic voters who "know they're safe" and redirect votes to favorites who need help. Result: strongest candidate sometimes fails to be elected.

System options:

Recommendation: Approval voting. Approving a deserving candidate never hurts them. Strategic misrepresentation requires complex reasoning about competitors' mutual approval rates — unlikely to be widespread. Implement with a threshold (e.g., elected if approved by >50% of voters) or seat-limit (top 3 by approval count).