AV Runoff Strategy Comparison

Explore strategic voting in runoff approval systems using constructions from Fishburn & Brams (1981) "Approval Voting, Condorcet's Principle, and Runoff Elections"

What this tool does:

This tool demonstrates Theorem 2 from the paper: for non-dichotomous preferences, every strategy is admissible under runoff approval voting. That means for any two ballot strategies you choose, we can construct concrete election scenarios where each beats the other—neither dominates!

The constructions use specific vote totals and pairwise matchups (H1-H4 from the proof) to show how runoff mechanics create complex strategic incentives.

Note: Rather than getting caught up in the "this is so unrealistic all the scenarios have candidates winning by one vote!", one might instead interpret the votes as follows:

100 votes: Frontrunner
99 votes: Viable but not leading
10 votes: Nonviable

What this tool shows is that when multiple candidates appear to be viable, it is mathematically proven that the addition of a runoff can add perverse strategic incentives depending on the perceived or predicted head-to-head matchups that would occur in the final top-two runoff.

Step 1: Define Your Preference

How to format your preference:

Separate candidates with > to show preference order (most preferred → least preferred)
At least 3 candidates required — the theorem applies to non-dichotomous preferences
Candidate names can contain letters, numbers, spaces, hyphens, and apostrophes
Spaces around > are optional but allowed

Examples:

Peltola>Begich>Palin — Alaska 2022 RCV election
A>B>C — simple abstract example
Alice>Bob>Charlie>Diana — 4 candidates with names
Candidate 1 > Candidate 2 > Candidate 3 — spaces are fine

Note: With only 2 tiers (dichotomous preferences like A>B), certain strategies dominate and the interesting non-dominance results don't always apply. You need at least 3 distinct preference levels to see the theorem in action (as we have implemented it here).

Enter preference order:

Approval Runoff Strategy Comparison Tool

Step 1: Define Your Preference

Step 2: Select Two Strategies to Compare

Strategy S

Strategy T