User:RalphInOttawa/Standard Vote
Standard Vote does IRV first (2 or 3 times) and pairwise comparisons second (only between runoff winners).
Standard Vote (abbreviated as SV) is an election vote-counting method that chooses a single candidate by using ranked ballots and the sequential elimination of lowest counting candidates in two or three runoffs. This addition to IRV addresses the unfairness inherent in a single runoff voting system, by identifying when the runner-up has a spoiler effect on the election and doing something about it.
This method modifies Instant Runoff Voting (IRV) by adding a second and possibly a third runoff with later-no-harm safeguards for runoff winners. It further modifies simple IRV by allowing the voter to mark more than one candidate at the same ranking level. These additions improve on simple IRV by: allowing voters to give a full and honest opinion, making this system more monotonic (Monotonicity), reducing the failure rate for the Independence of Irrelevant Alternatives (IIA), eliminating Center-squeeze, and making the practice of Favorite Betrayal unnecessary.
Description
Voters rank the candidates using as many ranking levels as there are candidates, or to a limit as specified by the electing authority. The Google spreadsheet demonstrator (link below) has five levels of ranking which makes it possible to compare apples to apples with some other voting systems.
Ballots are collected and recorded. Equal rankings on ballots are turned into ranked choices based on a random ordering of candidates. This is followed by the first runoff. Candidates are eliminated one at a time in each runoff, with the vote counts of the final two candidates compared (effectively pairwise) to identify a winner and a runner-up. The method continues with a second runoff, in which the first runoff's runner-up is immediately withdrawn. The voter's preferences trapped behind/under the runner-up are now countable like those of other voters whose first preference has lost. This identifies a second runoff winner. If the first winner repeats as the second winner, the decision is made to elect the first/second winner.
If no decision, a pairwise comparison is made of the first and second winners. The first winner will be elected if the second winner can do no better than a tie. Failing that, a third runoff occurs in which the first runoff's winner is immediately withdrawn, giving supporters of the first winner the same fairness that supporters of the runner-up received in the second runoff. This identifies a third winner. If the second winner repeats as the third winner, the decision is made to elect the second/third winner.
If no decision, a pairwise comparison is made of the second and third winners. If the third winner can do no better than tie the second winner, a decision is made to elect the second winner. If no decision, the third winner is compared pairwise with the first winner. If the third winner beats the first winner, the decision is made to elect the third winner. Finally, with no decision made, the result is a paradoxical tie between the three runoff winners. A decision is made to elect one of the three runoff winners by a "random draw".
Tie breakers
Random Voter Hierarchy (RVH) is used for each "random draw". Ideally these values are determined at the "instant" the counting begins, giving candidates and voters nothing to apply a strategy to. If two or more candidates have the same rank on any number of ballots, this tie is re-ranked by "random draw" en masse (all occurrences of A=B will either all count as A>B or all count as B>A). Ties encountered during elimination rounds will be decided by a second "random draw" applied in all elimination rounds. In comparing runoff winners, in the event of a tie, the earlier winner's count takes precedence over a subsequent winner's count. When thre's a paradoxical tie, the candidate to be elected will be decided using the third "random draw".
Proof of concept
Here's a shared link to a spreadsheet demonstrator (10 candidates, 1-5 picks, 200 voting rows. Note: you need to be signed on to a Google Account).
As of April 2024 I've made an Excel workbook for Excel users (10 candidates, 1-5 picks and 50 voting rows):
For those who can’t access these spreadsheets, here are short descriptions of SV's eleven step process.
1: Create 3 random draws of alternatives for use in steps 2, 3, 4, 7 and 11.
2: Convert equal ranking on ballots to ranked choices (using the 1st random draw to order equally ranked choices).
3: Execute a “normal” IRV runoff to identify the 1st winner and a runner-up (2nd random draw breaks ties).
4: Execute a 2nd IRV runoff without the runner-up from step 3, identifying a 2nd winner (2nd random draw breaks ties).
5: If the same alternative wins both runoffs, elect that alternative.
6: If the 1st winner does not lose to the 2nd winner, one on one, elect the 1st winner.
7: Execute a 3rd runoff without the 1st winner from step 3, identifying a 3rd winner (2nd random draw breaks ties).
8: If the same alternative wins the 2nd and 3rd runoffs, elect that alternative.
9: If the 2nd winner does not lose to the 3rd winner, one on one, elect the 2nd winner.
10: If the 3rd winner beats the 1st winner, one on one, elect the 3rd winner.
11: Elect one of the three runoff winners (3rd random draw to decide).
Examples comparing SV to IRV
This example shows a paradoxical tie. To be fair, SV gives each candidate an equal chance of election.
4 A>B
3 B>C
2 C>A
IRV elects A. SV decides who wins a three way tie (step 11).
The next example shows how Standard Vote does not suffer from center-squeeze.
4 A>C
3 B>C
2 C
IRV elects A. SV elects Candidate C (step 8).
The following example demonstrates that favorite betrayal is not necessary.
4 A>C
3 B>C
2 C>B
IRV elects B. SV elects C (step 8). No need to turn 2 A>C into 2 C>A.
The 4th example illustrates the system doing a lot better than IRV at not failing monotonicity.
8 A
5 B>A
4 C>B
IRV and SV elect B.
When 2 supporters of A change their votes to C (favorite betrayal):
6 A
2 C
5 B>A
4 C>B
IRV elects A. SV decides who wins the three way tie (step 11).
Using SV, the same result can be produced by simply having the 2 supporters of A add C to their ballots.
6 A
2 A>C
5 B>A
4 C>B
IRV elects B. SV decides who wins in the three way tie (step 11).