Purpose of VoteFair representation ranking
VoteFair representation ranking identifies the most-representative choice (which is the same as the most popular choice according to VoteFair popularity ranking), the second-most representative choice, and additional representation levels. The second-most representative choice is identified after appropriately reducing the influence of the voters who are well represented by the most-popular (and most-representative) choice. Without this adjustment the same voters who are well-represented by the most popular choice could also determine the second-place winner.
Calculation details for VoteFair representation ranking
This is a description of the full algorithm used to calculate VoteFair representation ranking results.
Here are the steps for calculating the first-most representative and second-most representative choices:
- Identify the most popular choice using VoteFair popularity ranking. This choice is the first-most representative choice.
- Identify the ballots that rank the first-most representative choice as their first (highest-ranked) choice.
- Completely ignore the ballots identified in step 2, and then use VoteFair popularity ranking to identify the most popular choice based on the remaining ballots. This choice will not necessarily be second-most representative. Instead, this choice is used in step 5 to identify which ballots are from voters who are well-represented by the first-most representative choice.
- Again consider all the ballots.
- Identify the ballots in which the first-most representative choice is preferred over the choice identified in step 3. This step identifies the ballots from voters who are well-represented by the first-most representative choice. With this criteria the only way for a voter to avoid having his or her ballot identified in this step is to express a preference that significantly reduces the chances that the preferred choice will be ranked as the most popular.
- Proportionally reduce the influence of the ballots identified in step 5. (This step reduces the influence of the voters who are well-represented by the first-most representative choice.) This calculation uses the following sub-steps:
- Start with the number of ballots that were identified in step 5.
- Subtract half the number of total ballots.
- The result represents the ballot-number-based influence deserved for the ballots identified in step 5.
- Divide the ballot-number-based influence number by the number of ballots identified in step 5.
- The result is the fraction of a vote that is allowed for each ballot identified in step 5.
- Based on all the ballots, but with reduced influence for the ballots identified in step 5, use VoteFair popularity ranking to identify the most popular choice among the remaining choices. This choice is the second-most representative choice.
If additional levels of VoteFair representation ranking are needed, these steps are repeated using the remaining choices.
To clarify the nature of the results, if VoteFair representation ranking is used in an election that involves voters who are somewhat equally balanced in their preference for Republican and Democratic candidates, and if the first-most representative candidate is a Republican, then the second-most representative candidate is likely to be a Democrat, the third-most representative candidate is likely to be another Republican, and the fourth-most representative candidate is likely to be another Democrat. In other words, the results basically alternate back and forth in terms of which voters get represented.
The VoteFair ranking calculation methods are in the public domain, but copyright protection (see below) applies to the above description.