Workbench Tabs

1. Tab: Ballots

Having opened a ballot file, the ballots are displayed in the Ballots tab:

This shows for each non-empty ballot-row in the file the numeric preference given to each candidate for each ballot, where “1” is highest-preference, “most-preferred.” The “Ballot #” is the 0-based row number within the file of the data for the given ballot:

This tab is not particularly interesting, but if you double-click on a particular ballot row it displays a dialog for the ballot represented by the given row:

The ballot dialog has two tabs, the first showing the “optical-reader” representation of the ballot, and the second showing how the given ballot would be tallied:

is preferred-more-than  :   is preferred-the-same-as

2. Tab: Tally

The per-ballot tallies shown above accrue to obtain a collective result for the file as a whole:

is preferred-more-than  :   is preferred-the-same-as

Such a tally might pertain to the results of a given poll, or individual-poll tallies can be accrued to obtain the results for the electoral district as a whole.

We assume in the workbench that the tally is for an electoral district as a whole.

3. Tab: Ranked Pairs

Once we have a tally for the given electoral district, we can determine majority and minority candidates for each one-to-one matchup between candidates, and then sort, or “Rank,” these pairwise-results (hence “Ranked Pairs”) according to strengths of preference, which we show here (along with the final result):

is preferred-more-than  :   is preferred-the-same-as

The final candidate rankings for the given set of ballots are shown in the pane on the right.

is preferred-more-than  :   is preferred-the-same-as

Selecting a candidate in the right-hand RP Result table will highlight on the left and on the previous Tally tab those pairs involving the given candidate.

Upon selecting the “Ranking Graph” (sub)tab, the candidate-rankings are displayed in a directed graph:

is preferred-more-than  :   is preferred-the-same-as

Selecting a given pair on the left will display the graphical evaluation up-to and including the selected pair:

is preferred-more-than  :   is preferred-the-same-as

In order to rank the pairs, we sort on:

  1. Majority Votes (descending), then on
  2. Minority Votes (ascending), then on
  3. Tally-Sheet Order (ascending)

Note that:

  • When the votes for both candidates in a given pair are equal, it is irrelevant which we choose as the “Minority” vs the “Majority” candidate
  • The minority-vote sort is only relevant for pairs that have the same majority-vote value; and
  • The Tally-order sort is only relevant for pairs that have, both the same majority-vote, and the same minority-vote values.
  • In a real election, which might involve tens of thousands of ballots, the tally-order sort is arguably highly unlikely to come into play.

The sort is part of the Ranked-Pairs algorithm for breaking preference cycles:

  1. In any case where there is a Condorcet winner, the sorting strategy is immaterial in determining the winner.
  2. In any case where there is not a Condorcet winner, however, it is used to break preference cycles on a rationale that a stronger-preferences should prevail over a weaker preference in any case where they cannot both be retained.

Taking each pair as defining a relationship between the two candidates of the pair, being that one is more-preferred than the other, or that they’re preferred the same, and applying “more preferred than” transitively, we can then determine a relative ranking among the candidates themselves.

This will usually be a linear ranking among all candidates, but does not categorically exclude ties in any given position; for a single-member election, however, only first place ties would be of any consequence.

4. Tab: Comparative Results

Finally, we compare the ranked-pairs result with the results as-if we interpret those ballots as a first-past-the-post (FPTP) election, and in terms of an Instant-Runoff Vote (IRV) election.

Note that we can only do this comparison because we’re capturing all the ballot data. If we were only capturing the ranked-pair tally results, we wouldn’t have sufficient information to do so.

This tab displays the rankings for each voting system. For IRV, which potentially entails multiple rounds of counting, you can see the results for each counting-round as well.

A candidate highlighted here will also be highlighted in the Ranked-Pairs (RP Result) tab and the tally tab so that you can see the specific pairwise match-ups that led to the given outcome.

Double-clicking on a given candidate here will bring up a result-summary page for that candidate:

Next: Results Notes

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