Multiple choice voting

[teacherteacher]

(Moderation note: This thread formerly appeared in the thread Primary school maths is sufficient for most day-to-day activities for most people. It was moved to its own thread because it wasn’t relevant to the original threads topic, but a topic of its own.)

In multiple choice tests, three-four answers are provided. How about when voting? If six choices are provided on a ballot, for only 115 total voters, isn't that providing invalid results? In other words, with so many choices (6), an unfair advantage may be given to a particular group? Help! I need this answered by tomorrow morning! $100,000 is riding on this for our school district! Thanks to anyone with info!! I'll even accept statistical theories for this one!

[freeztar]

Originally Posted by teacherteacher

In multiple choice tests, three-four answers are provided. How about when voting?

Voting is quite a bit different imho. Voting is driven by belief and emotion. Test questions are answered from knowledge or guessing.

If six choices are provided on a ballot, for only 115 total voters, isn't that providing invalid results?

What do you mean by "invalid results"? See below...

In other words, with so many choices (6), an unfair advantage may be given to a particular group?

I fail to see the logic in this. "More choices" generally implies an inversely direct relationship between success and the number of choices presented. Where does the "unfair" factor come into play?

Help! I need this answered by tomorrow morning! $100,000 is riding on this for our school district! Thanks to anyone with info!! I'll even accept statistical theories for this one!

What? Can you explain your presentation at all so we can have a chance of relating and subsequently offering help/advice?


Why not start a new thread for this subject? It would make a great philosophical topic, if structured appropriately.

[Michaelangelica]

Originally Posted by teacherteacher

In multiple choice tests, three-four answers are provided. How about when voting? If six choices are provided on a ballot, for only 115 total voters, isn't that providing invalid results? In other words, with so many choices (6), an unfair advantage may be given to a particular group? Help! I need this answered by tomorrow morning! $100,000 is riding on this for our school district! Thanks to anyone with info!! I'll even accept statistical theories for this one!

Could you please explain. I am confused by your question?
Is it optional preferential voting or first past the post?
Why 115 voters?
Why would there be an 'unfair' advantage?

You might get a better reply to your question if you posted it on the "homework" thread/forum
http://hypography.com/forums/science...-homework.html

[teacherteacher]

There are 40 voters committed to one choice. It is certain they will vote for choice #1. The remaining 75 voters are split (though not evenly) among choices #1,2,3,4,5&6. However, 46 of these 75 voters DO NOT want choice #1 and will NOT choose that, but will vote for one of #2-6. The 75 voters are trying to "beat out" the 40 voters, however, the 75 can't agree on which choice to go with and say just vote for anything other than #1. I say that's like voting for the Independent candidate - it's a wasted vote and gives the advantage to the other group. Any answers out there????

[CraigD]

Originally Posted by teacherteacher

There are 40 voters committed to one choice. It is certain they will vote for choice #1. The remaining 75 voters are split (though not evenly) among choices #1,2,3,4,5&6. However, 46 of these 75 voters DO NOT want choice #1 and will NOT choose that, but will vote for one of #2-6. The 75 voters are trying to "beat out" the 40 voters, however, the 75 can't agree on which choice to go with and say just vote for anything other than #1. I say that's like voting for the Independent candidate - it's a wasted vote and gives the advantage to the other group. Any answers out there????

This is an interesting example, which emphasizes how traditional consensus-finding tools can fail to provide "accurate" results.

In the above example, the tool in question is a “single round, one-vote-per-person, yes-only multiple-choice vote”. As teacher notes, this can result in the election of a political candidate that the majority of the voters don’t want.

There are many alternative tools to avoid this sort of result. I’ll summarize just a few:

Multi-round (“run-off”) voting.
Voting for the choices/candidates is done in, with the candidates receiving the fewest choices being dropped from the next vote.

Such a vote might look like this:

• Round 1: 49 for #1; 17 for #6; 15 for #3; 13 for #5; 11 for #2; 10 for #4
• Round 2: 49 for #1; 39 for #3; 27 for #6
• Round 3: 66 for #3; 49 for #1

Candidate #3 is elected, even though she/he was in 3rd place in the initial vote.

Ranking by preference
Each voter lists the candidates in order of their preference. A point value is assigned to each position. The candidate with the highest point total wins

Such a vote might look like this:

• Voter 1 (most to least preferred): 2, 6, 3, 5, 4, 1
• Voter 2: 3, 6, 5, 4, 2, 1
• Voter 3: 1, 2, 6, 3, 5, 4
• Voter 4: 5, 6, 2, 4, 3, 1
  …
• Voter 115: 1, 6, 2, 3, 4, 5

Using a simple point scheme of 6 for 1st place, 5 for 2nd place … 1 for 6th place, the results of this election would be

• 552 for #6; 483 for #2; 414 for #3; 368 for #5; 345 for #1; 253 for #4

Candidate #6 is elected, even though other candidates were ranked 1st by more voters.

”No” votes
Allow each voter 1 “yes” and 1 “no” vote.

Such a vote might look like:

• Candidate #3: 15 for – 9 against = 6 points
• Candidate #5: 13 for – 10 against = 3 points
• Candidate #4: 10 for – 7 against = 3 points
• Candidate #6: 17 for – 18 against = -1 points
• Candidate #2: 11 for – 13 against = -3 points
• Candidate #1: 49 for - 58 against = -9 points

Candidate #3 is elected, even though candidate #1 received the most “yes” votes, and candidate #4 the fewest “no” votes.

[freeztar]

At kvraudio.com, there is a monthly competition. Whoever participates must vote. The voting scheme is what CraigD defines above as "Ranking by preference". Imho, this voting scheme works very well within the constructs of the competition, but as always, YMMV.

"Say you were standing with one foot in the oven and one foot in an ice bucket. According to the percentage people, you should be perfectly comfortable." ~Bobby Bragan, 1963

[TheBigDog]

I like the idea of the run-off voting. The only difference I would make is that if a candidate got 50%+ of the vote in the first round it would be over. Otherwise you would eliminate the bottom candidates by some formula with each round.

The idea of one yes and one no is awful. If we had that then Ralph Nader would be president.

Bill

[CraigD]

Originally Posted by TheBigDog

The idea of one yes and one no is awful. If we had that then Ralph Nader would be president.

If the 2000 US Presidential had been simple “single round, one-vote-per-person, yes-only multiple-choice vote”, Al Gore would have won with 51,003,926 vs. George W. Bush with 50,460,110 and Ralph Nader with 2,883,105.

If we assume that all of the Gore votes would have been “Gore ‘yes’, Bush ‘no’”, all the Bush votes “Bush ‘yes’, Gore ‘no’”, all the Nader votes “Nader ‘yes’, Bush ‘no’”, and all the rest “their candidate ‘yes’, Gore ‘no’”, the “one yes and one no” score would have been:

• Gore: 51,003,926 - 384,516 - 98,022 - 83,702 - 54,652 = 50,383,034
• Bush: 50,460,110 - 2,883,105 = 47,577,005
• Nader: 2,883,105 – 0 = 2,883,105

A Gore win.

But, of course, US Presidential elections are decided by neither of these methods, but by the rather complicated Electoral College. In the atypical case of the 2000 election, it was decided to some extent by the Supreme Court and a host of other officials and agencies.

[TheBigDog]

Originally Posted by CraigD

If the 2000 US Presidential had been simple “single round, one-vote-per-person, yes-only multiple-choice vote”, Al Gore would have won with 51,003,926 vs. George W. Bush with 50,460,110 and Ralph Nader with 2,883,105.

If we assume that all of the Gore votes would have been “Gore ‘yes’, Bush ‘no’”, all the Bush votes “Bush ‘yes’, Gore ‘no’”, all the Nader votes “Nader ‘yes’, Bush ‘no’”, and all the rest “their candidate ‘yes’, Gore ‘no’”, the “one yes and one no” score would have been:

• Gore: 51,003,926 - 384,516 - 98,022 - 83,702 - 54,652 = 50,383,034
• Bush: 50,460,110 - 2,883,105 = 47,577,005
• Nader: 2,883,105 – 0 = 2,883,105

A Gore win.

But, of course, US Presidential elections are decided by neither of these methods, but by the rather complicated Electoral College. In the atypical case of the 2000 election, it was decided to some extent by the Supreme Court and a host of other officials and agencies.

You didn't subtract all the "no" votes from Bush and Gore.

Gore = (as calculated) 50,383,034 - 50,460,110 = -77,076
Bush = (as calculated) 47,577,005 - 51,003,926 = -3,426,921
Nader = 2,883,105

Nader wins over Gore by nearly 3 million votes.

Bill

[CraigD]

Originally Posted by TheBigDog

You didn't subtract all the "no" votes from Bush and Gore.

Gore = (as calculated) 50,383,034 - 50,460,110 = -77,076
Bush = (as calculated) 47,577,005 - 51,003,926 = -3,426,921
Nader = 2,883,105

Nader wins over Gore by nearly 3 million votes.

Wow! You’re correct. A big omission on my part

All hail president Ralph!

Of course, if such a scheme were actually used, people would be aware that Nader had a chance of winning, and might have voted “Nader no” in significant numbers. Assuming that 3,000,000 “Gore yes” voters voted “Nader no”, and 500,000 of them voted “Buchanan no” (a lot of Gore supporters disliked Buchanan even more than Bush), the winner would have been…

• Gore = (as calculated) 50,383,034 – (50,460,110) = -77,076
• Bush = (as calculated) 47,577,005 – (51,003,926 -3,500,000) = 73,079
• Nader = 2,883,105 – 3,000,000 = -116,895
• Pat Buchanan = 449,225 -500,000
• Harry Brown = 384,516

... Libertarian candidate Harry Brown?!

Realizing this, no votes might shift to Brown, and so on, until the election became an exercise in candidates coordinating their voters’ no votes, or an effective “randomocracy”.

Though mostly a Tacoma Park, MD phenomena, some may remember William Brown’s ca. 1990 weekly comic ”President Bill”, which chronicled the fictional administration of the first and last randomly elected US Executive, the largely autobiographical “Bill”.

Based on this, I’m forced to agree with Bill’s (hypography’s, not these various other’s) assessment of the “one yes, one no” voting tool as “awful” – at least for electing presidents.