Your conclusions are correct, but I don't know why you'd need to consider surface area at all. Ultimately, isn't it the amount of carbon sequestered directly proportional to the mass of the grown plant? I don't know what percentage of a tree is carbon, but if the tree weighs a ton you multiply that percentage by one ton, and you have the answer. Ignoring what are probably small differences in carbon percentage, I'd think a one-ton pine tree would sequester as much carbon as a one-ton oak tree, even with different foliage surface areas.
I don't think the point is that you can buy a "better" box; just that you can buy a box of your own, period, without losing some features due to the lack of 2-way communications in the 1st-generation cable cards.
Can you tell me how a Tivo is better than a Motorola box? I've never used Tivo, but my cable company-supplied Motorola works well. Sometimes I wish it had more storage, though.
Oh, Tivo. I was assuming one would buy a Motorola cable box/DVR. Last time I checked, though, those were around $700, not $500, but they could have come down since then.
But the advantage of having a two-way cable card is that you can access the cable company's TV schedules, isn't it? If you don't use Tivo's schedules, can you waive the subscription fee, or is it still mandatory?
$5/month for the card, and $500 upfront plus $20/month for the box
I'm confused. Was that a typo, or do you really mean we would be paying a monthly rental for the box (in addition to rental for the card) after buying it?
In the episode where Fry tried to use the professor's F-Ray to find the winning Slurm bottle cap, at one point the F-Ray was pointed at Bender's head and revealed a 6502 (just watched this episode again the other day, thanks to Cartoon Network's recent marathon). So Beer Brewing Bender's designers knew what they were doing.
I didn't get into the full details of approval voting strategy on purpose, to keep the discussion focused. But if you want the details...
To decide how you vote for candidate X, you calculate the expected utility for all candidates excluding X, and compare X's utility to that value. To calculate expected utility, you need to know your ratings of each candidate and the odds that each candidate will win (getting the latter information is going to be tricky, though).
Let's say your true ratings are 100 for Paul, 95 for Obama, and 0 for Clinton. You know you will vote 100 for Paul and 0 for Clinton, but what do you vote for Obama? You need to look at the chances of Paul getting more approval votes than Clinton. Let's say Clinton and Paul have equal chances. Then your expected utility of the outcome, ignoring Obama, is 50. Obama's utility is higher than 50, so you would vote 100 for Obama in this case, because defeating the Clinton threat is more important.
On the other hand, if it's more of an Obama/Paul race, and Clinton's chances are negligible, the calculation gives a different result. Let's say (again ignoring Obama) that Paul has a 20:1 chance of beating Clinton. Then the expected utility of the outcome, minus Obama, is 95.23 (20*100/21). In that case, your best choice in that election is to rate Obama 0.
Sometimes, you may have no clue as to the probabilities involved. Without a priori information, you would just do the calculation assuming the candidates have equal odds. Or you might have polling information only (e.g., Paul's approval = 55%, Obama's approval = 55%, and Clinton's approval = 35%). Then you decide which candidates are viable, and which are not, and just do the calculation for the viable candidates, ignoring the nonviable.
The study used a 50/50 mix of honest/strategic voters. I'm not saying range voting wouldn't be better than approval in such a mix. I'm saying (perhaps speculatively) that 50/50 mixes aren't realistic; my instincts tell me it would be closer to 10/90. I'm also saying that if one group of voters (say the Democratic Party) is more inclined to vote honestly than the other group (say the Republicans), then 3rd party candidates aligned with the Republicans have a better chance of being elected. This would probably lower the social utility (increase the Bayesian regret), especially if Democrats are the majority. In the simulation, the distribution of honest and strategic voters was random.
In range voting, any voter trying for an optimum strategy (i.e., maximizing his expected utility) is going to give 100% ratings to the candidates that boost his expected utility, and 0% to candidates that hurt it. There is no in between (in the case where a candidate has a neutral contribution to the expected utility, the voter can put any number between 0% and 100% for that candidate, but such cases are rare enough to ignore for practical purposes). The voter has no incentive to give a 45% or 55% rating to a candidate; 0% or 100% will always be a better strategy. So if all voters pursue their best strategies, the outcome of range voting will match that of approval.
If we assume some voters are going to be "altruistic" and reduce the effect of their vote by giving true ratings, then yes, range voting will yield different results from approval voting. But this is false altruism. Say 55 voters have similar preferences, and another 45 voters have preferences similar to each other but different from the preferences of the first group. Suppose 10 of the first group weaken their votes by giving intermediate ratings to some candidates, and suppose none of the second group do so. The "altruistic" voters are sacrificing not just their own interests, but the interest of the other members of their own party, and the second group wins in spite of smaller numbers by having a more aggressive strategy.
That is why I prefer the real fairness of approval voting to the pretense of greater accuracy given by range voting.
You're half-right. But just because all rational voters would cast what amounts to an approval ballot in a range-voting election does not mean its busted. That conclusion is based on the assumption that approval voting itself is busted. But approval voting provides exactly the same fairness benefit as range voting, minus the illusion of a higher-resolution ballot. In fact, approval voting is just a special case of range voting, with only 1 bit of resolution on the ballot for each candidate.
So I wouldn't say range voting is busted. I would just say it's approval voting in disguise.
Arrgh. You can't really measure strengths of preferences among individuals in a 2-candidate election (and with more than 2 candidates, you can't measure those strengths either, but with the additional information contained in the ballots -- if they aren't lone-mark plurality ballots -- you can begin to hypothesize). People with very weak preferences will just sit it out. You have to assume that those who do care to vote have strong preferences. There's no fair and accurate way to determine that voter A's preference is stronger than voter B's. The fact that they bothered to vote entitles them to have their vote counted on an equal basis with the other voters.
In a sense, you can game approval voting just as you say. But it turns out to be very benign gaming. It simply means the voter adjusts his or her threshold of approval, based on circumstances. Suppose we held the Democratic primaries with approval voting. Then the ABC crowd could approve all the candidates except Clinton, and the Clinton crowd could approve Clinton only. Without Clinton in the race, or if Clinton simply didn't appear to be a viable candidate, the ABC crowd would probably just vote for their favorite two or three candidates, and the Clinton crowd would vote their favorite two or three. This sort of strategizing can indeed change the outcome, but voters are unlikely to regret their strategies. Also, in this scenario, in fact in ANY approval voting scenario, nobody ever has an incentive to disapprove their second choice while approving their third choice. Thus, voters are always honest about the preferences they do express in such a system.
1) Majority Property: If over 50% of voters prefer a single candidate over all others than that candidate should win the election.
2) Condorcet Winners Criterion: If a candidate would win any head-to-head election then that candidate should win the election.
3) Condorcet Losers Criterion: If a candidate would lose every head-to-head election then that candidate should not win the election.
Some people may consider those important. I don't. Just to take the majority property: If there is a candidate with greater than 50% first-preference support, that candidate will get greater than 50% in an approval election. Lets say she gets 55%. But she might have 45% of the last-preference votes. The majority criterion says she should win, but if 65% of voters approve a second candidate, then that candidate has the benefit of pissing off 10% fewer voters. Why sacrifice that benefit to the rather arbitrary majority criterion? Of course, approval voting simply doesn't allow anyone to express an order of preference between two candidates except by approving one and disapproving the other. Instead, it allows each voter to set a threshold above which candidates are tolerable, and below which they are not. This is a simple power, but a far more useful one to the individual voter than providing ordinal rankings.
The Condorcet criteria have problems, too. My second-ranked candidate may be nonetheless completely unacceptable to me. Why should the supporters of that candidate benefit from that fact that I ranked him second? I may actually be tempted to put my third-choice candidate second, because my third choice might be less viable and this could increase my first choice's chances of winning in certain scenarios.
Arrow's theorem implies that EVERY voting system has MAJOR flaws. This includes range voting, instant runoff, etc.
No, it doesn't imply that at all. Arrow chose 5 criteria and showed that no ranked voting system can meet all 5 of these. He did not show that no non-ranked voting can meet all 5 (and some of them don't even apply to non-ranked systems). Moreover, he did not show that failing to meet each of his criterion constitutes a "MAJOR flaw". There are many who view the IIA criterion as insignificant, for instance. I do, for this reason: If you add (or remove) a candidate from the race, then the preferences expressed on the ballots provide more (or less) information as a result. Suppose I list my preferences as A > B > C > D. Now you add candidate E to the race. My new list could be A > B > E > C > D. This signals a higher likelihood that I consider the difference between B and D more significant than the difference between A and B. (It's not a certainty, but it becomes statistically significant when there are many voters with similar patterns). If the addition of candidate E changes the winner from C to B because a significant number of people vote like me, then this should be considered a plus, not a minus.
In place of IIA, I'd rather see a criterion that recognizes the fact that, if candidate 1 beats candidate 2, but candidate 1 beats candidate 3 by a smaller margin than the margin by which candidate 2 beats candidate 3, or if candidate 3 beats candidate 1 while candidate 2 beats candidate 3 (both cases are possible in ranked systems), then the information about candidate 3 does not support (and in fact contradicts) the result of candidate 1 beating candidate 2. In which case, removing candidate 3 from the race should not cause the resulting social rankings of the first two candidates to be reversed. That is a narrower criterion than IIA (which says removing candidate 3 should never change the social ranking of candidate 1 relative to candidate 2, even if the margins of candidate 3 relative to candidates 1 and 2 do support the given outcome), and one which can be met by a number of methods (including range voting and its special case, approval voting).
Too many people look at Arrow's Theorem and conclude, as you did, that it precludes any satisfactory voting system from being designed, but it does no such thing.
My CD changer (Yamaha) ejects immediately. The DVD player (Panasonic) may take about a second, I think. But there's that glass door thing (not an issue for everybody, I admit), so even if it took 20 seconds, I'd still be there doing it manually.
They aren't taking a pro-electronic voting position. They are challenging a new system that they think does not comply with state law. They have taken the position of requiring a paper trail when touch-screen voting systems are used. Their concern here (if it is correctly placed; I'm not familiar enough with the law and circumstances in Ohio) seems consistent with their earlier positions.
The article is not about electronic voting. It's about an optical-scan voting system that is implemented in a way that may not comply with state law (something that it is up to a court to decide).
Eject? It's the one button I don't want to see on a remote.
I have a glass door in front of my components. I don't want to accidentally eject into the closed door, so I intentionally left the eject functons for the CD and DVD players off when I set up my Harmony remote.
And think about it: When you eject a disc, you're going to want to be right there in front of the device to remove the disc and/or put in a new one. Why do you need the remote for this?
Nasty. I never liked the idea of catching traffic violators with cameras. I see it as a due process violation. In order to defend myself against the charges (if I choose to do so), I would actually need to remember the specifics of the event, which I'm not likely to be able to do if I get a citation in the mail 3 days after the fact.
I bet Legolas shows up in the movie. He's a woodland elf, and Bilbo and the dwarves pass through their kingdom. Aragorn will show up, too. He spent much of his youth in Rivendell, about the time of Bilbo's journey, so why not? And Gimli won't be in the dwarf party, but knowing Jackson, he'll probably show up at the Battle of Five Armies. LotR characters will turn up in the movie because they are bound to be crowd pleasers.
Here, I'll fix it for you: "Well, in the plug-in hybrid case it's not so simple."
With non-plug-in hybrids (Prius, Civic, Accord, Camry, etc.), the state-of-charge varies very little from one fill-up to the next (mine is almost always 6 or 7 bars out of 8, except after steep uphill or downhill segments); the distance that small variance will take you is probably not going to exceed a mile or two. So, distance driven divided by the amount of gas you feed it is going to be pretty darned accurate.
An article linked from that article suggests otherwise. And lest you object that that article is discussing mathematical models only, read the current article linked from the story: "The team developed a mathematical model to show the impact of unexpected events such as a lorry pulling out of its lane on a dual carriageway." Does a model count as knowledge?
Hmm...That might actually work, except for one thing: People routinely ignore speed limits. Maybe they don't in the UK? And they don't in Mississippi. I drove through that state once, and nobody was going faster that 65 MPH. I saw one guy get pulled over. Must have been doing 65.1, because he wasn't passing other traffic.
That's an interesting suggestion. My take on it (having spent a lot of time looking at these methods a few years back) is that eliminating half of the candidates all at once, instead of one round at a time, could change the order of elimination of the remaining candidates, and changing the order of elimination can change the final outcome. Example -- 10 candidates, and your method eliminates candidates F, G, H, I, and J all at once. But perhaps IRV would eliminate candidate E instead of candidate F in the fifth step, leaving candidates A, B, C, D, and F. Performing the remaining steps of IRV with A, B, C, D, and E might not yield the same results as with A, B, C, D, and F.
Really, it's a problem with elimination methods in general -- small changes that cause eliminations to occur in different orders can change the final result.
Your argument is exactly why I like approval voting. In approval voting, if people don't strategize, then their vote reflects their conscience. But even if they do strategize, then their vote still reflects their conscience. Because the only form of strategy that works in approval voting is adjusting the cutoff point: I can approve my favorite candidate, or I can approve my two favorites, or my three favorites, and so on, but (as long as I am a rational voter) I will never approve my 1st and 3rd choices while disapproving my 2nd choice.
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the surface area of its foliage for absorbing CO2
Your conclusions are correct, but I don't know why you'd need to consider surface area at all. Ultimately, isn't it the amount of carbon sequestered directly proportional to the mass of the grown plant? I don't know what percentage of a tree is carbon, but if the tree weighs a ton you multiply that percentage by one ton, and you have the answer. Ignoring what are probably small differences in carbon percentage, I'd think a one-ton pine tree would sequester as much carbon as a one-ton oak tree, even with different foliage surface areas.
It's auto-self-redundant.
Microsoft Is Constantly Reinventing Operating Systems to Obsolete Future Technology.
OK, somebody else try to do better.
I don't think the point is that you can buy a "better" box; just that you can buy a box of your own, period, without losing some features due to the lack of 2-way communications in the 1st-generation cable cards.
Can you tell me how a Tivo is better than a Motorola box? I've never used Tivo, but my cable company-supplied Motorola works well. Sometimes I wish it had more storage, though.
Oh, Tivo. I was assuming one would buy a Motorola cable box/DVR. Last time I checked, though, those were around $700, not $500, but they could have come down since then.
But the advantage of having a two-way cable card is that you can access the cable company's TV schedules, isn't it? If you don't use Tivo's schedules, can you waive the subscription fee, or is it still mandatory?
$5/month for the card, and $500 upfront plus $20/month for the box
I'm confused. Was that a typo, or do you really mean we would be paying a monthly rental for the box (in addition to rental for the card) after buying it?
In the episode where Fry tried to use the professor's F-Ray to find the winning Slurm bottle cap, at one point the F-Ray was pointed at Bender's head and revealed a 6502 (just watched this episode again the other day, thanks to Cartoon Network's recent marathon). So Beer Brewing Bender's designers knew what they were doing.
I didn't get into the full details of approval voting strategy on purpose, to keep the discussion focused. But if you want the details...
To decide how you vote for candidate X, you calculate the expected utility for all candidates excluding X, and compare X's utility to that value. To calculate expected utility, you need to know your ratings of each candidate and the odds that each candidate will win (getting the latter information is going to be tricky, though).
Let's say your true ratings are 100 for Paul, 95 for Obama, and 0 for Clinton. You know you will vote 100 for Paul and 0 for Clinton, but what do you vote for Obama? You need to look at the chances of Paul getting more approval votes than Clinton. Let's say Clinton and Paul have equal chances. Then your expected utility of the outcome, ignoring Obama, is 50. Obama's utility is higher than 50, so you would vote 100 for Obama in this case, because defeating the Clinton threat is more important.
On the other hand, if it's more of an Obama/Paul race, and Clinton's chances are negligible, the calculation gives a different result. Let's say (again ignoring Obama) that Paul has a 20:1 chance of beating Clinton. Then the expected utility of the outcome, minus Obama, is 95.23 (20*100/21). In that case, your best choice in that election is to rate Obama 0.
Sometimes, you may have no clue as to the probabilities involved. Without a priori information, you would just do the calculation assuming the candidates have equal odds. Or you might have polling information only (e.g., Paul's approval = 55%, Obama's approval = 55%, and Clinton's approval = 35%). Then you decide which candidates are viable, and which are not, and just do the calculation for the viable candidates, ignoring the nonviable.
The study used a 50/50 mix of honest/strategic voters. I'm not saying range voting wouldn't be better than approval in such a mix. I'm saying (perhaps speculatively) that 50/50 mixes aren't realistic; my instincts tell me it would be closer to 10/90. I'm also saying that if one group of voters (say the Democratic Party) is more inclined to vote honestly than the other group (say the Republicans), then 3rd party candidates aligned with the Republicans have a better chance of being elected. This would probably lower the social utility (increase the Bayesian regret), especially if Democrats are the majority. In the simulation, the distribution of honest and strategic voters was random.
In range voting, any voter trying for an optimum strategy (i.e., maximizing his expected utility) is going to give 100% ratings to the candidates that boost his expected utility, and 0% to candidates that hurt it. There is no in between (in the case where a candidate has a neutral contribution to the expected utility, the voter can put any number between 0% and 100% for that candidate, but such cases are rare enough to ignore for practical purposes). The voter has no incentive to give a 45% or 55% rating to a candidate; 0% or 100% will always be a better strategy. So if all voters pursue their best strategies, the outcome of range voting will match that of approval.
If we assume some voters are going to be "altruistic" and reduce the effect of their vote by giving true ratings, then yes, range voting will yield different results from approval voting. But this is false altruism. Say 55 voters have similar preferences, and another 45 voters have preferences similar to each other but different from the preferences of the first group. Suppose 10 of the first group weaken their votes by giving intermediate ratings to some candidates, and suppose none of the second group do so. The "altruistic" voters are sacrificing not just their own interests, but the interest of the other members of their own party, and the second group wins in spite of smaller numbers by having a more aggressive strategy.
That is why I prefer the real fairness of approval voting to the pretense of greater accuracy given by range voting.
You're half-right. But just because all rational voters would cast what amounts to an approval ballot in a range-voting election does not mean its busted. That conclusion is based on the assumption that approval voting itself is busted. But approval voting provides exactly the same fairness benefit as range voting, minus the illusion of a higher-resolution ballot. In fact, approval voting is just a special case of range voting, with only 1 bit of resolution on the ballot for each candidate.
So I wouldn't say range voting is busted. I would just say it's approval voting in disguise.
Arrgh. You can't really measure strengths of preferences among individuals in a 2-candidate election (and with more than 2 candidates, you can't measure those strengths either, but with the additional information contained in the ballots -- if they aren't lone-mark plurality ballots -- you can begin to hypothesize). People with very weak preferences will just sit it out. You have to assume that those who do care to vote have strong preferences. There's no fair and accurate way to determine that voter A's preference is stronger than voter B's. The fact that they bothered to vote entitles them to have their vote counted on an equal basis with the other voters.
In a sense, you can game approval voting just as you say. But it turns out to be very benign gaming. It simply means the voter adjusts his or her threshold of approval, based on circumstances. Suppose we held the Democratic primaries with approval voting. Then the ABC crowd could approve all the candidates except Clinton, and the Clinton crowd could approve Clinton only. Without Clinton in the race, or if Clinton simply didn't appear to be a viable candidate, the ABC crowd would probably just vote for their favorite two or three candidates, and the Clinton crowd would vote their favorite two or three. This sort of strategizing can indeed change the outcome, but voters are unlikely to regret their strategies. Also, in this scenario, in fact in ANY approval voting scenario, nobody ever has an incentive to disapprove their second choice while approving their third choice. Thus, voters are always honest about the preferences they do express in such a system.
1) Majority Property: If over 50% of voters prefer a single candidate over all others than that candidate should win the election.
2) Condorcet Winners Criterion: If a candidate would win any head-to-head election then that candidate should win the election.
3) Condorcet Losers Criterion: If a candidate would lose every head-to-head election then that candidate should not win the election.
Some people may consider those important. I don't. Just to take the majority property: If there is a candidate with greater than 50% first-preference support, that candidate will get greater than 50% in an approval election. Lets say she gets 55%. But she might have 45% of the last-preference votes. The majority criterion says she should win, but if 65% of voters approve a second candidate, then that candidate has the benefit of pissing off 10% fewer voters. Why sacrifice that benefit to the rather arbitrary majority criterion? Of course, approval voting simply doesn't allow anyone to express an order of preference between two candidates except by approving one and disapproving the other. Instead, it allows each voter to set a threshold above which candidates are tolerable, and below which they are not. This is a simple power, but a far more useful one to the individual voter than providing ordinal rankings.
The Condorcet criteria have problems, too. My second-ranked candidate may be nonetheless completely unacceptable to me. Why should the supporters of that candidate benefit from that fact that I ranked him second? I may actually be tempted to put my third-choice candidate second, because my third choice might be less viable and this could increase my first choice's chances of winning in certain scenarios.
Arrow's theorem implies that EVERY voting system has MAJOR flaws. This includes range voting, instant runoff, etc.
No, it doesn't imply that at all. Arrow chose 5 criteria and showed that no ranked voting system can meet all 5 of these. He did not show that no non-ranked voting can meet all 5 (and some of them don't even apply to non-ranked systems). Moreover, he did not show that failing to meet each of his criterion constitutes a "MAJOR flaw". There are many who view the IIA criterion as insignificant, for instance. I do, for this reason: If you add (or remove) a candidate from the race, then the preferences expressed on the ballots provide more (or less) information as a result. Suppose I list my preferences as A > B > C > D. Now you add candidate E to the race. My new list could be A > B > E > C > D. This signals a higher likelihood that I consider the difference between B and D more significant than the difference between A and B. (It's not a certainty, but it becomes statistically significant when there are many voters with similar patterns). If the addition of candidate E changes the winner from C to B because a significant number of people vote like me, then this should be considered a plus, not a minus.
In place of IIA, I'd rather see a criterion that recognizes the fact that, if candidate 1 beats candidate 2, but candidate 1 beats candidate 3 by a smaller margin than the margin by which candidate 2 beats candidate 3, or if candidate 3 beats candidate 1 while candidate 2 beats candidate 3 (both cases are possible in ranked systems), then the information about candidate 3 does not support (and in fact contradicts) the result of candidate 1 beating candidate 2. In which case, removing candidate 3 from the race should not cause the resulting social rankings of the first two candidates to be reversed. That is a narrower criterion than IIA (which says removing candidate 3 should never change the social ranking of candidate 1 relative to candidate 2, even if the margins of candidate 3 relative to candidates 1 and 2 do support the given outcome), and one which can be met by a number of methods (including range voting and its special case, approval voting).
Too many people look at Arrow's Theorem and conclude, as you did, that it precludes any satisfactory voting system from being designed, but it does no such thing.
My CD changer (Yamaha) ejects immediately. The DVD player (Panasonic) may take about a second, I think. But there's that glass door thing (not an issue for everybody, I admit), so even if it took 20 seconds, I'd still be there doing it manually.
They aren't taking a pro-electronic voting position. They are challenging a new system that they think does not comply with state law. They have taken the position of requiring a paper trail when touch-screen voting systems are used. Their concern here (if it is correctly placed; I'm not familiar enough with the law and circumstances in Ohio) seems consistent with their earlier positions.
The article is not about electronic voting. It's about an optical-scan voting system that is implemented in a way that may not comply with state law (something that it is up to a court to decide).
Eject? It's the one button I don't want to see on a remote.
I have a glass door in front of my components. I don't want to accidentally eject into the closed door, so I intentionally left the eject functons for the CD and DVD players off when I set up my Harmony remote.
And think about it: When you eject a disc, you're going to want to be right there in front of the device to remove the disc and/or put in a new one. Why do you need the remote for this?
Nasty. I never liked the idea of catching traffic violators with cameras. I see it as a due process violation. In order to defend myself against the charges (if I choose to do so), I would actually need to remember the specifics of the event, which I'm not likely to be able to do if I get a citation in the mail 3 days after the fact.
I bet Legolas shows up in the movie. He's a woodland elf, and Bilbo and the dwarves pass through their kingdom. Aragorn will show up, too. He spent much of his youth in Rivendell, about the time of Bilbo's journey, so why not? And Gimli won't be in the dwarf party, but knowing Jackson, he'll probably show up at the Battle of Five Armies. LotR characters will turn up in the movie because they are bound to be crowd pleasers.
I'll bet Jobs can afford it.
Here, I'll fix it for you: "Well, in the plug-in hybrid case it's not so simple." With non-plug-in hybrids (Prius, Civic, Accord, Camry, etc.), the state-of-charge varies very little from one fill-up to the next (mine is almost always 6 or 7 bars out of 8, except after steep uphill or downhill segments); the distance that small variance will take you is probably not going to exceed a mile or two. So, distance driven divided by the amount of gas you feed it is going to be pretty darned accurate.
An article linked from that article suggests otherwise. And lest you object that that article is discussing mathematical models only, read the current article linked from the story: "The team developed a mathematical model to show the impact of unexpected events such as a lorry pulling out of its lane on a dual carriageway." Does a model count as knowledge?
Hmm...That might actually work, except for one thing: People routinely ignore speed limits. Maybe they don't in the UK? And they don't in Mississippi. I drove through that state once, and nobody was going faster that 65 MPH. I saw one guy get pulled over. Must have been doing 65.1, because he wasn't passing other traffic.
That's an interesting suggestion. My take on it (having spent a lot of time looking at these methods a few years back) is that eliminating half of the candidates all at once, instead of one round at a time, could change the order of elimination of the remaining candidates, and changing the order of elimination can change the final outcome. Example -- 10 candidates, and your method eliminates candidates F, G, H, I, and J all at once. But perhaps IRV would eliminate candidate E instead of candidate F in the fifth step, leaving candidates A, B, C, D, and F. Performing the remaining steps of IRV with A, B, C, D, and E might not yield the same results as with A, B, C, D, and F.
Really, it's a problem with elimination methods in general -- small changes that cause eliminations to occur in different orders can change the final result.
Your argument is exactly why I like approval voting. In approval voting, if people don't strategize, then their vote reflects their conscience. But even if they do strategize, then their vote still reflects their conscience. Because the only form of strategy that works in approval voting is adjusting the cutoff point: I can approve my favorite candidate, or I can approve my two favorites, or my three favorites, and so on, but (as long as I am a rational voter) I will never approve my 1st and 3rd choices while disapproving my 2nd choice.