Table of Content
- Getting Started
- Introduction: IRV RAs with RAIRE
- IRV elections and Visualizing Outcomes
- Assertions for IRV winners
- Risk Limiting Audits
- Using assertions to audit IRV outcomes
- Margin and Difficulty
Margin and Difficulty
Assertion Margins
This section describes how to implement the Assertion Margins component. In order to estimate sample sizes, we need to understand the concept of "margin" as it applies to an assertion, or rather to the two-candidate contest described by that assertion.
The Assertion Margin for an assertion A is simply the sum of the scores of all ballots for A. This is the minimum number of ballots that would have to be added or removed to switch a true assertion to false.
The Assertion Margin mA for assertion A and a set of ballots B is:
mA(B) = Σb ∈ B SCOREA(b)
This margin can be used directly to calculate the diluted margin μ for each assertion, in order to estimate the required sample size. The diluted margin for an IRV contest is the smallest diluted margin for any of its assertions.
Estimating the difficulty of auditing an assertion
Given a set of assertions that attacks an outcome, the 'easiest to audit' assertion is the one we expect would require the smallest sample of ballots to audit. Given two assertions, we assume that the assertion with the larger diluted margin will be the easier one to audit. For the purposes of our running example, we will define the diluted margin of an assertion with winner w and loser l as the difference in tallies of the winner and loser divided by the total number of ballots cast.
Recall that when we talk about the winner and loser of an assertion, we are not referring to the ultimate winners and losers of the election—we are just referring to the candidates being compared by the assertion itself.
In our example, the total number of cast ballots is 13500. Let's also assume that we are undertaking a ballot level comparison audit, and use 1 divided by the diluted margin to estimate the auditing difficulty of a given assertion.