Condorcet method, Charts to aid evaluation, Sample elections, And more comparison to IRV

(FYI There are links to related posts way down toward the bottom.)

A summary of my Condorcet ranked choice election evaluation process:

1. Check for a Condorcet winner. (One who wins head-to-head against all other candidates.) (Includes a majority winner of first-choice votes.)
If there is one, they win.

2. Narrow down a large field of candidates, using first-choice votes.

3. Use head-to-head matches of two candidates at a time, and tally each candidate’s wins. One with the most match wins wins the election.

4. Use tiebreakers. If a tiebreaker fails to eliminate a candidate, proceed to the next tiebreaker, in this order.
– If two tied for most wins, the match between them can resolve it.
– IRV to eliminate one. (A match of more than two.)
– First-choice votes.
– Random flip.

Election example, 100 voters

First, a list of the 31 ballot types. The numbers shows how many ballots of each type. The letters show 1st, 2nd, and 3rd choice in order.

2 A (Two voters said A 1st, no one 2nd or 3rd.)
2 AB (Two voters said A 1st, B 2nd, no one 3rd.)
2 ABC
6 AC
5 ACB
2 ACD

1 B
1 BA
2 BAD
14 BD

2 C
3 CA
7 CAE
4 CB
2 CE

2 D
7 DB
3 DBA
4 DBC
4 DBE

7 EC
3 ECD
4 EDC
1 EF
1 EFC

2 FE
2 FEB

1 GH
1 GHB

1 HA
2 HCB

I have generated two charts that should help people understand and document the process.

There are three pictures of the first chart. The numbers on all three are the same, and are from the list of ballots above. The captions tell how to use the chart.

The above caption shows a shortcut for scoring a head-to-head match, which makes the thought of a hand recount much more pleasant.

The next chart shows a way of tracking the results of all possible head-to-head matches.

The next part is related to the charts, because they show an example in which IRV could easily elect the wrong candidate.

Comparison of IRV to a Condorcet method

Here are three “elections” that are very similar, as they differ by only one vote. All three have the same Condorcet winner, but different IRV winners.

The Condorcet records of the top 5, in all three elections, are:
C 7-0 (7 head-to-head match wins, 0 losses)
B 6-1
D 5-2
A 4-3
E 3-4
(Note that E cannot beat A, B, C, or D head-to-head. E has 3 wins only because there are 3 longshot candidates. More longshot candidates in the race could make E look even better, and E’s chance of winning would still be nil.)

Election 1
Votes are as shown in the chart (G2, H3, etc).
C has 18 1st choice votes.

C is the Condorcet winner (beats every candidate in head-to-head matches).
In an IRV system, C is also the winner, beating D in the final match.
This means IRV has agreed with Condorcet.

A vs B vs C vs D vs E
20 19 20 20 20 – B eliminated

A vs C vs D vs E
23 20 34 20 – E eliminated
E actually tied C, but C won the head-to-head tiebreaker.
(If there were no tiebreaker, they would both be eliminated, and D would win the final against A.)

A vs C vs D
23 31 38 – A eliminated

C vs D
46 40 – C wins election 1.

Election 2
Same as election 1, but one voter stayed home, so there are now 99 voters instead of 100.
C lost a vote, and now has 17 1st choice votes.

D is now the IRV winner.
C is still the Condorcet winner, but came in 4th.
B would beat everyone except C, and got 5th.

A vs B vs C vs D vs E
20 19 19 20 20 – B eliminated (loses tiebreaker to C, but C goes out next, so it doesn’t really matter.)

A vs C vs D vs E
23 19 34 20 – C eliminated

A vs D vs E
33 34 22 – E eliminated. The 4th best candidate is A, but A gets to the final.

A vs D
33 41 – D wins election 2.

Election 3
The same as election 1, with 100 voters, but one 1st choice vote has changed from C to B.
C has 17 1st choice votes, and B now has 19.

Although C is still the Condorcet winner, IRV eliminates C in 5th place.
The final is A vs B, and B wins.

E is the worst candidate of the top 5, and gets 3rd place again.
The 2nd worst, A, makes it into the final 2 again.

A vs B vs C vs D vs E
20 20 19 20 20 – C eliminated

A vs B vs D vs E
30 26 20 22 – D eliminated

A vs B vs E
30 44 22 – E eliminated

A vs B
30 46 – B wins election 3.

IRV puts too much importance on first-choice votes, and is vulnerable to vote splitting.
It is not reliable, not until the final round. The final works because it is head-to-head.

Recap:
The voters prefer C over every candidate in all 3 elections, if they are compared head-to-head (Condorcet method).
There is no justification for any other candidate beating C.
And B should beat every candidate except C.
Elections 1, 2, and 3, should be C>B>D>A>E

Using IRV destabilizes the outcome. IRV apparently sees these three elections as virtual ties that could go either way, when they are clearly not.
Election 1, C>D>A>E>B (C wins, B is last of the top 5)
Election 2, D>A>E>C>B (D wins, C and B place 4th and 5th)
Election 3, B>A>E>D>C (B wins, C is last of the top 5)

C goes from first to fifth!

A link to my full Condorcet method procedure: https://americarepair.home.blog/practical-condorcet-method/

A link back to the related blog post: https://americarepair.home.blog/2020/09/02/condorcet-is-a-better-ranked-choice/

Brief Summary of this election method: https://americarepair.home.blog/2020/12/13/brief-summary-of-practical-condorcet-election/