I'm not sure what your example is designed to prove. Yes, voters make their votes stronger by strategically normalizing them (and taking some additional steps if they are really vicious). We actually DEFINE max and min scores as "your most and least preferred", by definition. It really makes no sense for someone NOT to have at least one minimum score and one maximum, except in the weak sense that people's inherent sense of applying a logarithmic scale to their scores (diminishing returns, so to speak) may actually produce greater utility. We could add another strategy generator to the computer program and test that, or probably even test in using a spreadsheet.
In any case, it could be that Jane really does HATE the first candidate, hence the 1, and Joe might give a 7, 8, and 9, meaning he'd be fairly pleased with ANY of those candidates. It's good for voters to be honest, because then we have a better chance of electing a candidate who gives the most happiness to the most people.
As for magical optimum winner, that is the winner based on the highest UTILITY average (or total, depending on how you want to look at it - same thing).
Here's an example spreadsheet where I have the table on the right automatically set to act as a rescaled version of the actual utility values.
Notice that the range voting winner here is Candidate 5, even though C1 produces a much greater average happiness. As we see, even Range Voting isn't perfect.
Now let's see who wins if we use honest plurality - everyone casts a vote for his sincere favorite. C5 ties with C1, each getting 2 votes. So what if voters had used the normal plurality strategy of casting their vote for their favorite just between the two front-runners (we'll pretend there are no insanely idealistic Nader spoiler people). C5 beats C1 4-2! So strategic plurality also elects C5. C5 produces a social utility of 38.86% here. If we try a bunch of different voting methods, we might find one that, in just this particular case, DOES elect C1, producing 100% social utility efficiency. But to make that mean something, we have to do hundreds, thousands, or even millions of different scenarios, to approximate the random feelings that voters have based on the random ways they were brought up, or the random books or experiences that might have just affected their beliefs, or the random candidates who might have happened to run that year, or the random smear ads that the voters might have happened to see. So many random things affect those utilities.
But hopefully this example helps demonstrate how the magical winner is not always the same as the Range Voting winner. RV just does a much better job than other methods at maximizing the utility.
Re: Erroneously?
In any case, it could be that Jane really does HATE the first candidate, hence the 1, and Joe might give a 7, 8, and 9, meaning he'd be fairly pleased with ANY of those candidates. It's good for voters to be honest, because then we have a better chance of electing a candidate who gives the most happiness to the most people.
As for magical optimum winner, that is the winner based on the highest UTILITY average (or total, depending on how you want to look at it - same thing).
Here's an example spreadsheet where I have the table on the right automatically set to act as a rescaled version of the actual utility values.
http://spreadsheets.google.com/pub?key=pXPf6D8HwIWncwYJKKb4CcQ
Notice that the range voting winner here is Candidate 5, even though C1 produces a much greater average happiness. As we see, even Range Voting isn't perfect.
Now let's see who wins if we use honest plurality - everyone casts a vote for his sincere favorite. C5 ties with C1, each getting 2 votes. So what if voters had used the normal plurality strategy of casting their vote for their favorite just between the two front-runners (we'll pretend there are no insanely idealistic Nader spoiler people). C5 beats C1 4-2! So strategic plurality also elects C5. C5 produces a social utility of 38.86% here. If we try a bunch of different voting methods, we might find one that, in just this particular case, DOES elect C1, producing 100% social utility efficiency. But to make that mean something, we have to do hundreds, thousands, or even millions of different scenarios, to approximate the random feelings that voters have based on the random ways they were brought up, or the random books or experiences that might have just affected their beliefs, or the random candidates who might have happened to run that year, or the random smear ads that the voters might have happened to see. So many random things affect those utilities.
But hopefully this example helps demonstrate how the magical winner is not always the same as the Range Voting winner. RV just does a much better job than other methods at maximizing the utility.
Regards,
Clay