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R1 | R2 | R3 | R4 | R5 | R6 | R7 | R8 | R9 | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
148 | 5 | -2 | 3 | 0 | 3 | 0 | 3 | 0 | 3 | 0 | 3 | 0 | 3 | 0 | 3 | 0 | 3 |
CPT004 | 1 | 0.3999999999999999 | 1.4 | 0 | 1.4 | 0 | 1.4 | 0 | 1.4 | 1 | 2.4 | 1 | 3.4 | -0.3999999999999999 | 3 | 0 | 3 |
CPT003 | 2 | 0.3999999999999999 | 2.4 | 0 | 2.4 | 0 | 2.4 | 0 | 2.4 | 0 | 2.4 | 0 | 2.4 | 0.16470588235294104 | 2.564705882352941 | 0 | 2.564705882352941 |
715 | 1 | 0.3999999999999999 | 1.4 | 0 | 1.4 | 0 | 1.4 | 0.3999999999999999 | 1.7999999999999998 | 0 | 1.7999999999999998 | 0 | 1.7999999999999998 | 0.11764705882352944 | 1.9176470588235293 | 0 | 1.9176470588235293 |
CPT001 | 1 | 0.3999999999999999 | 1.4 | 0 | 1.4 | 0 | 1.4 | 0 | 1.4 | 0 | 1.4 | 0 | 1.4 | 0.11764705882352944 | 1.5176470588235293 | 0 | 1.5176470588235293 |
CPT006 | 1 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 1 | -1 | 0 | 0 | 0 | 0 | 0 |
CPT005 | 1 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 1 | -1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
532 | 0 | 0.4 | 0.4 | 0 | 0.4 | 0 | 0.4 | -0.4 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
167 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
731 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
Total | 12 | 12 | 12 | 12 | 12 | 12 | 12 | 12 | 12 | ||||||||
Inactive Ballots | 0.00000 | 0.00000 | 0.00000 | 0.00000 | 0.00000 | 0.00000 | 0.00000 | 0.00000 | 0.00000 |
1st ch | 2nd ch | 3rd ch | 4th ch | 5th ch | |
---|---|---|---|---|---|
148 | 5 | 2 | 3 | 1 | 0 |
167 | 0 | 0 | 0 | 0 | 0 |
CPT006 | 1 | 0 | 0 | 3 | 2 |
532 | 0 | 2 | 2 | 3 | 0 |
715 | 1 | 2 | 1 | 0 | 2 |
731 | 0 | 0 | 0 | 0 | 0 |
CPT001 | 1 | 2 | 1 | 1 | 2 |
CPT003 | 2 | 1 | 2 | 3 | 3 |
CPT004 | 1 | 2 | 3 | 1 | 1 |
CPT005 | 1 | 1 | 0 | 0 | 1 |
Total Choices | 12 | 12 | 12 | 12 | 11 |
RCV123 on-line system handles ties among candidates facing elimination differently than any official RCV systems. (Other than tiebreaking, we use the WIGM RCV system that is the standard counting method.)
We vary from official RCV for tiebreaking because in elections with thousands or hundreds of thousands of voters, ties are very unlikely. But our mission is to make RCV helpful to anyone who wants to make a group decision – including smaller groups with perhaps only 25 voters in a classroom or small civic organization. In a small group election with five candidates and 20 voters, for example, there are very likely to be several ties as the rounds progress.
Official RCV uses random chance to settle any ties. We believe it would be unsatisfying for small voting groups to find that much of the outcome was determined by random chance.
So we developed a unique tiebreaking system that calculates a single number for each candidate based on their vote totals and the choice column they are in. The candidate with the highest tiebreaking number wins that tie. If that tiebreaker number winds up in a tie, then RCV123 resorts to random chance.
Each first-choice vote is worth 100, and each subsequent choice is worth 2/3 (.67) of the previous choice on a ballot. Then all the votes and weighting for each candidate in each column are totaled to determine an overall tiebreaker number. So in our method, for example, three 2nd place votes are worth very slightly more than two 1st place votes. But it would take 37 10th place votes to have the same weight as one 1st place vote.
Our tiebreaking method looks at all choice data from every ballot. This is different from the rounds of counting - which only looks at the data from each round as it is calculated. For example, in actual rounds of counting, a candidate with zero first-choice votes will be eliminated right away, and any 2nd or 5th or 10th place votes they may have does not matter at all.
If two candidates facing elimination have a tie, and have identical tiebreaker numbers, then RCV123 will use random chance to decide. We create a grid of randomly decided, head-to-head tiebreaking match-ups for each combination of candidates. That grid can be found on the results page of any election.
The use of the mathematical tie breakers will be noted in election results with a blue rectangle over vote totals in that round for the candidates involved. The use of the last-resort, random tie breaker will be noted by the color green.
We believe our tiebreaking system is a good compromise between not weighting the choice column of votes at all, and excessively weighting one choice column vs. another immediately adjacent.
This table shows the primary tiebreaker calculation. It uses the raw ballot data before any rounds are tabulated.
The number of voters who chose a candidate as their first choice is added to the number of voters who chose the candidate as their second, third, etc. choice, with each count given approximately 2/3 of the weight given to the previous count. Then all the columns are added together to arrive at a tiebreaker value for each candidate.
1st | × 1.00 | 2nd | × 0.67 | 3rd | × 0.45 | 4th | × 0.30 | 5th | × 0.20 | Tiebreaker Value | |
---|---|---|---|---|---|---|---|---|---|---|---|
148 | 5 | 5.00 | 2 | 1.34 | 3 | 1.35 | 1 | 0.30 | 0 | 0.00 | 7.99 |
167 | 0 | 0.00 | 0 | 0.00 | 0 | 0.00 | 0 | 0.00 | 0 | 0.00 | 0.00 |
CPT006 | 1 | 1.00 | 0 | 0.00 | 0 | 0.00 | 3 | 0.90 | 2 | 0.40 | 2.31 |
532 | 0 | 0.00 | 2 | 1.34 | 2 | 0.90 | 3 | 0.90 | 0 | 0.00 | 3.14 |
715 | 1 | 1.00 | 2 | 1.34 | 1 | 0.45 | 0 | 0.00 | 2 | 0.40 | 3.19 |
731 | 0 | 0.00 | 0 | 0.00 | 0 | 0.00 | 0 | 0.00 | 0 | 0.00 | 0.00 |
CPT001 | 1 | 1.00 | 2 | 1.34 | 1 | 0.45 | 1 | 0.30 | 2 | 0.40 | 3.49 |
CPT003 | 2 | 2.00 | 1 | 0.67 | 2 | 0.90 | 3 | 0.90 | 3 | 0.60 | 5.07 |
CPT004 | 1 | 1.00 | 2 | 1.34 | 3 | 1.35 | 1 | 0.30 | 1 | 0.20 | 4.19 |
CPT005 | 1 | 1.00 | 1 | 0.67 | 0 | 0.00 | 0 | 0.00 | 1 | 0.20 | 1.87 |
Total Choices | 12 | 12 | 12 | 12 | 11 |
In case the above system can’t break a tie, RCV123 generates a randomly ordered list of the candidates. That order is fixed when the ballot is created.
Order | |
---|---|
148 | 9 |
167 | 4 |
CPT006 | 3 |
532 | 7 |
715 | 2 |
731 | 1 |
CPT001 | 6 |
CPT003 | 8 |
CPT004 | 5 |
CPT005 | 10 |
Raw vote totals do not include votes rejected by the Election Administrator