How do you choose a winner in an election?

[singularity6]

I'll try to keep this relatively short and simple, but it at least slightly appropriate to post now.

If you are holding an election with more than 2 choices, then there is no way of finding a winner that satisfies all the fairness criterion. Most elections are between more than 2 candidates, so every election we run is mathematically imperfect, so if you read this, don't be upset. It's just the way the world works! Also note that when I teach this stuff, we usually spend a couple weeks in the class room working on this, so if it seems hard to understand just by reading a couple paragraphs... well, it's math! There are plenty of resources online for you to explore. Keep in mind that Wikipedia might not be the easiest one to read, however!

Let's unpack this a bit... What are these fairness criterion, anyway?

1. Majority Rule - The choice with the majority of the first place votes wins. This can be a problem when there are more than 2 choices as it's very possible that neither choice receives the majority of the vote. One might think that the most votes should suffice... but if you think about it, let's say that in an election between 3 people, 100 voters voted, and it turned out like this:

31 people for A, 40 people for B and 29 people for C

Is it fair that B won when the majority of voters voted against?

2. The Condorcet Criterion - The choice that beats all other choices in one-on-one match-ups prevails. Runoff votes, where look at one-on-one comparisons and eject the loser in each pairing can violate this; someone might be second choice in one scenario and ejected too early (loosely speaking, kinda like Survivor.)

3. Monotonicity - I had a hard time summarizing this one, so I will swipe this from the internet:

If an election is held and a winner is declared, this winning candidate should remain the winner in any revote in which all preference changes are in favor of the winner of the original election.

Three students, Al, Bob, and Carrie are running for class president. The class will vote in rounds. The student with the fewest votes in the first round will drop out and a new vote will be taken between the two remaining candidates. The student with the most votes in this final round will be declared the winner of the election. In the first round, Al gets 11 first place votes, Bob gets 8 first place votes, and Carrie gets 10 first place votes. Bob drops out (since he had the fewest votes in the first round). In the final round, Al gets 11 first place votes and Carrie gets 18 first place votes. Carrie wins the election!

 

But wait! The chairman of the election oversight committee destroyed the ballots before the results had been officially certified by the administration. You guessed it! The election had to be repeated. In the first round of the repeated election everyone voted exactly as in the first round of the original election except for 4 voters who decided to jump on the bandwagon and vote for Carrie instead of Al. As a result, Al gets 7 first place votes, Bob gets 8 first place votes, and Carrie gets 14 first place votes. This causes Al to drop out instead of Bob so that the final round of the repeated election is between Bob and Carrie. BUT the 7 students who originally voted for Al prefer Bob over Carrie. So, all 7 of them cast their votes for Bob in the final round. This gives Bob 15 votes and Carrie 14 votes. Bob wins the repeated election EVEN THOUGH THE ONLY CHANGES IN VOTER PREFERENCE WERE THE 4 VOTES THAT CHANGED FROM AL TO CARRIE (THE ORIGINAL WINNER). This illustrates a violation of the Monotonicity Criterion.

4. The Independence of Irrelevant Alternatives Criterion - This one is also a bit hard to explain, but here's a stab at it... If there are 3 ore more choices, and a choice is declared winner in one election, the same choice should be declared winners in any recount where one or more of the losing choices were removed. In other words, a loser dropping out shouldn't shuffle the votes to help one of the other losers win.

[sensei8]

Very interesting topics, thank you for starting it, singularity6!!

The political engine needs a tune-up across the board. But how does one know what's the fairest criteria to support, and is that preferred criteria the correct one??

It's, to me, like Mechanic 'A' says this and Mechanic 'B' says that and Mechanic 'C' says another, but to whomever, they all sound good and quite plausible, even after doing some research, does one vote for in the end?? Picking straws?? Eeny, meeny, miny, moe?? Gut feelings?? Hair on the back of my neck?? Paper, Rock, Scissors?? Flip a coin??

Sad and/or funny at the same time, those methods of choosing above, are exactly how choices are made by the voters at large.

Elections at the SKKA, at the Governing Body of Shindokan, where I'm the elected Kaicho, are conducted via the Roberts Rule of Order, Nominations and Elections rules. As a matter of fact our entire nuts and bolts of how the SKKA is conducted is based on Roberts Rule of Order and our By-Laws.

http://westsidetoastmasters.com/resources/roberts_rules/chap12.html

Soke and Dai-Soke created our By-Laws, which have been amended quite many times through the 60 years history that the SKKA has been functioning, but still, SKKA meetings and the like are strictly in and through Roberts Rule of Order, with no exceptions!!

Elections are held once every 4 years, depending on the office, whereas some offices are elected once every 3 years, and other offices are elected once every 2 years.

Within our Executive Team, Administration Team, General Affairs Team, and the Instructors Team lies the bulk of SKKA's Higher Hierarchy; each and every Director and the like are elected to their respective office.

Here's a small glimpse of SKKA's structure...

https://www.karateforums.com/a-glimpse-into-a-hombu-vt36501.html?highlight=glimpse

Please keep in mind that some changes have been made within the SKKA and our By-Laws since I first wrote the post that's linked directly above this paragraph. For example, both Soke and Dai-Soke have passed away, the attempted destruction of the SKKA/Hombu was staved off, new By-Laws and the like at the Restructuring of its Chartership, and the passing's of 6 members of the SKKA's Higher Hierarchy, to name just a few.

What type of criteria does the SKKA fall into, from the criteria that singularity6 has mapped out?? Majority Rule!! This criteria has been satisfied by our Legal Team. The other criteria mapped out by singularity6 are perfectly plausible, depending on ones particular situation(s).

Our Legal Team IS NOT comprised from any entity within the SKKA whatsoever!! Our Legal Team is an outside source; a Lawyer firm that's been contracted by both parties, SKKA and the Lawyer firm. No party of the outside Lawyer firm is ever allowed to become a student of any SKKA affiliated dojo, including, and especially, the Hombu for any reason whatsoever!! This provides both parties the highest integrity clauses possible.

Edited December 3, 2017 by sensei8

[JR 137]

Math people...

What’s the answer here?

[sensei8]

What's your opinion, if any, about Black's System??

[singularity6]

What's your opinion, if any, about Black's System??

Are you referring to the two-method system that uses the Condorcet winner, if one exists, but switches to a Borda count if one does not?

[MatsuShinshii]

What's your opinion, if any, about Black's System??

Are you referring to the two-method system that uses the Condorcet winner, if one exists, but switches to a Borda count if one does not?

I know we all study Martial Arts but when you speak Chinese the rest of us Okinawan and Japanese practitioners can't understand.

No seriously you totally lost me.

[sensei8]

What's your opinion, if any, about Black's System??

Are you referring to the two-method system that uses the Condorcet winner, if one exists, but switches to a Borda count if one does not?

I know we all study Martial Arts but when you speak Chinese the rest of us Okinawan and Japanese practitioners can't understand.

No seriously you totally lost me.

You're on a roll there, MatsuShinshii, you're on a roll!!

[sensei8]

What's your opinion, if any, about Black's System??

Are you referring to the two-method system that uses the Condorcet winner, if one exists, but switches to a Borda count if one does not?

Yes!!

[singularity6]

What's your opinion, if any, about Black's System??

Are you referring to the two-method system that uses the Condorcet winner, if one exists, but switches to a Borda count if one does not?

Yes!!

I'm fine with it. Both methods involved are easy enough to understand (for transparency) and easy enough to apply. I also prefer them to some of the various run-off methods, as those can sometimes harshly eject good candidates.

[sensei8]

What's your opinion, if any, about Black's System??

Are you referring to the two-method system that uses the Condorcet winner, if one exists, but switches to a Borda count if one does not?

Yes!!

I'm fine with it. Both methods involved are easy enough to understand (for transparency) and easy enough to apply. I also prefer them to some of the various run-off methods, as those can sometimes harshly eject good candidates.

Don't you just love a good game of politics??