I have a math degree (in fact, we're both in the same general field, aren't we?), and I'm mopping my brains off the floor too. ;)
In what respect? You mean to say that the material is too complicated? Too boring? What exactly is your complaint?
Not to mention, this "social utility efficiency" catchphrase they keep bandying about in their comments here strikes me as so much Boardroom Bingo.
No, it's a measure of your expected value, in the "currency" of satisfaction, with each voting method. A higher social utility efficiency means YOU, Joe Voter, will tend to be happier with the results of elections using Range Voting. Compared to IRV, the effect is enormous. Going from IRV to Range Voting gives you almost as big an increase in your expected satisfaction, as going from random selection to IRV in the first place.
I even took a look at their example, and all I see is that a hypothetical candidate who was left off of three ballots and named last on two others ends up winning. I hardly think a system where a candidate wins whom more than half of the voters absolutely don't want is an effective system.
Leaving someone off the ballot means that you aren't affecting his average, and is generally only done by voters when they don't know enough about that candidate to make an informed decision. In this example, Amy and Bob were extremely disliked by 3 people, whereas Cal was only strongly disliked by two people, and got an almost perfect score from three others, and a very high score from the other. So the most people are the most happy with Cal. The X voters chose to trust the opinions of more informed voters about a candidate they knew little about; but that's their choice, they could have strategically chosen to give Cal a 0 if they wanted.
Contrary to your intuition, this actually is the most effective system, because the paradoxes that arise using other methods tend to be MUCH worse. Look at this IRV election for example (IRV is the method you currently use), where the four voting blocs sit on a left-to-right axis as follows:
Leftist Centrist Rightist Dean Gore Bush 1 2 3 4
21 Bush > Gore > Dean 10 Gore > Bush > Dean 10 Gore > Dean > Bush 20 Dean > Gore > Bush
With IRV, Gore is eliminated, and Bush beats Dean 31-30. But wait! Gore is preferred to Bush 40-21 - a bigger percentage than any landslide election in our history. IRV picks the wrong winner in this scenario. As a result, the utility efficiency of IRV is significantly lower than that produced by Range Voting.
You can do simulations for yourself if you like, and see which methods tend to leave voters most satisfied. What you'll find is that Range Voting is a very large improvement over IRV, even if we can find special scenarios where Range Voting doesn't seem to pick the winner that you intuitively feel should win the election. On the whole Range Voting picks better winners. As a result, YOU will be happier with the results of elections if you use Range Voting. Choosing NOT to use it is just shooting yourself in the foot. It's like choosing to pick the winner at random instead of holding elections.
Look at this: http://spreadsheets.google.com/pub?key=pXPf6D8HwIWncwYJKKb4CcQ
You can easily set up a spreadsheet like that, and plug in lots of random utility values, and calculate the utility efficiency of plurality, strategic plurality, honest/scaled Range Voting, IRV, strategic IRV (same general strategy as with plurality), etc. etc. You can see the results for yourself. There will be cases when Range Voting picks a worse winner than plurality, but more often than not, it will be vice versa. Range Voting will simply decimate the other methods. Again, I encourage you to test this for yourself. Don't take my word for it. Practice the scientific method.
no subject
In what respect? You mean to say that the material is too complicated? Too boring? What exactly is your complaint?
Not to mention, this "social utility efficiency" catchphrase they keep bandying about in their comments here strikes me as so much Boardroom Bingo.
No, it's a measure of your expected value, in the "currency" of satisfaction, with each voting method. A higher social utility efficiency means YOU, Joe Voter, will tend to be happier with the results of elections using Range Voting. Compared to IRV, the effect is enormous. Going from IRV to Range Voting gives you almost as big an increase in your expected satisfaction, as going from random selection to IRV in the first place.
I even took a look at their example, and all I see is that a hypothetical candidate who was left off of three ballots and named last on two others ends up winning. I hardly think a system where a candidate wins whom more than half of the voters absolutely don't want is an effective system.
Leaving someone off the ballot means that you aren't affecting his average, and is generally only done by voters when they don't know enough about that candidate to make an informed decision. In this example, Amy and Bob were extremely disliked by 3 people, whereas Cal was only strongly disliked by two people, and got an almost perfect score from three others, and a very high score from the other. So the most people are the most happy with Cal. The X voters chose to trust the opinions of more informed voters about a candidate they knew little about; but that's their choice, they could have strategically chosen to give Cal a 0 if they wanted.
Contrary to your intuition, this actually is the most effective system, because the paradoxes that arise using other methods tend to be MUCH worse. Look at this IRV election for example (IRV is the method you currently use), where the four voting blocs sit on a left-to-right axis as follows:
Leftist Centrist Rightist
Dean Gore Bush
1
2
3
4
21 Bush > Gore > Dean
10 Gore > Bush > Dean
10 Gore > Dean > Bush
20 Dean > Gore > Bush
With IRV, Gore is eliminated, and Bush beats Dean 31-30. But wait! Gore is preferred to Bush 40-21 - a bigger percentage than any landslide election in our history. IRV picks the wrong winner in this scenario. As a result, the utility efficiency of IRV is significantly lower than that produced by Range Voting.
You can do simulations for yourself if you like, and see which methods tend to leave voters most satisfied. What you'll find is that Range Voting is a very large improvement over IRV, even if we can find special scenarios where Range Voting doesn't seem to pick the winner that you intuitively feel should win the election. On the whole Range Voting picks better winners. As a result, YOU will be happier with the results of elections if you use Range Voting. Choosing NOT to use it is just shooting yourself in the foot. It's like choosing to pick the winner at random instead of holding elections.
Look at this: http://spreadsheets.google.com/pub?key=pXPf6D8HwIWncwYJKKb4CcQ
You can easily set up a spreadsheet like that, and plug in lots of random utility values, and calculate the utility efficiency of plurality, strategic plurality, honest/scaled Range Voting, IRV, strategic IRV (same general strategy as with plurality), etc. etc. You can see the results for yourself. There will be cases when Range Voting picks a worse winner than plurality, but more often than not, it will be vice versa. Range Voting will simply decimate the other methods. Again, I encourage you to test this for yourself. Don't take my word for it. Practice the scientific method.
Clay