This vastly increases your ability to put information into the system.
This looks wrong to me. If two candidates participate in the election and one of them wins, the system has received 1 bit of information from all the voters combined. This doesn't depend on the voting scheme. If some intermediate stage of the voting scheme collects more information from each voter, then some later stage must throw that information away, because the system doesn't retain any information except which candidate got chosen.
Or did you imply some other technical meaning of "putting information into the system"? If so, could you explain your definition in more detail?
Yes, at the end only one candidate is selected, but the information isn't 'thrown away' - the MP now knows, rather than just "52% of people in the constituency voted for me", "27% of people voted for me as their first preference, with the Greens as their second preference, 25% voted for the Greens first and me second, and nobody at all voted for the Tories first and me second, or me second and the Tories first. That means that I'd better pay attention to my environmental policies, which I share with the Green, and maybe not so much my economic policies, which I share with the Tory".
Or, to look at it another way, the system does throw away all but one bit of information, but the information going into the system is used to tell it which bits to throw away.
We do, but they're usually not very inaccurate, and they also don't directly impact on a politician keeping her job. If you know that 27% of people in the country quite like the Greens but not as much as the Tories (or whoever) that's one thing. If you know that 27% of the people whose votes you need in order to stay in power like the Greens, that's a very different piece of information.
So why not just have polls that ask that question? It's not that expensive to get a YouGov to run a poll; much less than running a referendum is.
Because just asking the question doesn't actually affect their job. Otherwise why not just have a dictator and a lot of polls? The whole point is that this information is used to select MPs. (BTW I made a typo in the previous response - "usually not very inaccurate" should be "usually not very accurate").
Here you said that the advantage of AV was that politicians knew more about who voted for them, whose votes they needed, etc. I pointed out that there are easier ways of getting this information. Asking the question doesn't directly affect their job, but neither do all those extra votes.
In both systems, you have an election, and then a bunch of extra information, which the MP can find useful/make them take into account other voters. In one system, this extra information is gathered at the ballot, in the other, in separate polls. There's no other relivant difference except that one is cheaper (and monotonic!)
Your dictator response is mistaken because both systems have a No-dictator part; the bit at the ballot where an MP is elected. But both also have a separate 'more information' part, which was why you prefered AV - but which seems to be done better by independant polling.
No, because the information here changes the result of the election. That's the whole point...
Now you're making a different argument - you have to show that making your decide_winner function take more arguments is going to improve the quality of the output, and it's far from clear it will. You could put more information into the system by asking every voter to list their favourite colour, but unless you can show that this would actually improve the output, it's irrelivant.
Having more information can allow us to have more accurate beliefs, but it's not the case that putting more marks on a ballot paper will lead to a better result, especially when you're pushing against Arrow.
Agreed with the first paragraph, but the second one sounds strange. Does it really matter so much whether I enter 1 bit into the computer, or 10 bits telling it which 9 of them should be thrown away?
I see your point, but think of it this way. Say you're buying a new car, you'll probably only buy one car. But you might browse a handful of websites, maybe read What Car? magazine. That information contributes to the decision, and isn't 'thrown away', even though you end up just buying one car.
I'm frankly not awake enough to put things any more rigorously (I ran out of melatonin two days ago and my new order hasn't yet arrived, so I'm dopey as hell), but I hope this handwavey pseudo-explanation gets the point across.
Argh. If they're going to switch voting system, they should switch to a good one! And instant runoff is emphatically not a good voting system, because it is non-monotonic; rating a candidate higher may cause that candidate to lose. Which will eventually happen and cause a controversy. The right voting system to switch to is approval voting: rather than rank candidates, just check off all the candidates you like, and each of those candidates gets one vote. It's simple, votes have predictable consequences, and political positions of the form "I like " can be translated directly into ballots with minimal effort.
That's what I thought. At least some countries do use AV-like or proportional-representation systems in practice. (Australia uses AV in the House, proportional per state in the Senate.)
If I get it right, what you are looking for ist http://en.wikipedia.org/wiki/Cumulative_voting and http://en.wikipedia.org/wiki/Panachage, here in Hessen, a state of germany, I did it last week.
No, cumulative voting is the same system but in multi-member, rather than single-member, constituencies. The system being referred to is http://en.wikipedia.org/wiki/Approval_voting
Unfortunately according to Arrow's theorem, you can't have a perfect system. Non-monotonicity is, in my view, a reasonable trade-off for the extra information about preferences that gets put into the system. Approval voting also means some people's votes count more than others (a criticism that has been falsely raised against AV). Either way, the choice being presented isn't between all possible voting systems (I'd support STV myself) but between FPTP and AV, so I'm only discussing that choice rather than a choice over all voting-system space...
Arrow's theorem only applies to ordinal voting systems. It has nothing to say about range voting, e.g.
Isn't this the fallacy of gray? I agree that the disadvantages of AV over Condorcet are entirely irrelevant on 5 May, but that's not to say that a Condorcet system wouldn't be clearly superior. The only advantage of AV is that people would find a transition to STV easier to understand.
It is, but I was pointing out that "AV has downsides" isn't itself an argument. Approval voting, of course, isn't a Condorcet system either. In fact it can pick the Condorcet loser - even in a situation with a strong Nash equilibrium.
Approval voting, of course, isn't a Condorcet system either. In fact it can pick the Condorcet loser - even in a situation with a strong Nash equilibrium.
Really? This isn't obvious to me, and a quick attempt to construct a counterexample has failed and Google doesn't turn anything up either. Could you give a hint about how to construct this?
I got the result from http://dimacs.rutgers.edu/Workshops/DecisionTheory2/laslier.pdf . This deals with the preferences of the voters as utility functions (in such a way that it's not all that easy for me to turn it into "X voters want candidate Y"), but has at least one example that would elect the Condorcet winner with probability only 1/64 while the Condorcet loser would be elected with probability 31/64...
Makes sense, though we probably couldn't have got that through a referendum. Any preferential system is preferable (to me) to a non-preferential system, though (barring trivially absurd cases of both, like a preferential system where the least-preferred candidate wins).
Arrow's theorem has overly restrictive assumptions. It allows the voter to specify that A > B > C, but not that 50% chance of A plus 50% chance of C is better than B. If you relax these assumptions and allow each voter to specify their preferences over all weighted combinations of outcomes (aka specify a VNM utility function), then you can satisfy all desiderata of Arrow's theorem. The simplest scheme is just giving each user 1 vote and allowing them to assign portions of that vote to different candidates, e.g. 0.7 of my vote goes to A and 0.3 to B. The candidate with the highest sum of votes wins.
ETA: this system satisfies independence of irrelevant alternatives only in a certain overly restrictive sense, so it's not satisfactory. See the comment thread with Khoth and the links there.
You might be right (though I've never seen that objection before). I'll have to think it out. However, I think in that circumstance, you'd have a massive incentive to put all your vote onto one candidate who is most likely to win out of the choices you prefer, because anything else would be splitting the vote (in a way that you can't split a vote under AV, because your lower preferences only get counted if your higher ones have already been knocked out). So in practice, that system would collapse into something very like FPTP.
I'm skeptical of this, in that there are voting systems like this (10 seats open, you get ten votes to distribute however you want, etc.) and while they are limited by integer choices, they don't come close to satisfying the desiderata.
One thing that comes to mind is that it would be quite gameable; putting all your vote in one candidate will often be a better decision than comes to mind, but this is off the top of my head and it does seem within the realm of possibility that it could be "Arrow's no integral points on ideal voting systems theorem." Which is a great name for a theorem.
How does that satisfy independence of irrelevant alternatives? Candidate C can steal votes from candidate A, allowing B to win where A would have won otherwise.
It satisfies independence of irrelevant alternatives in the following sense: if A has more total vote than B, and you tweak each voter's individual allocations in any way but without touching their allocations toward A and B, you can't make B have more total vote than A. The proof is obvious. I'm not sure what you mean by vote-stealing, or by independence of irrelevant alternatives for that matter. Please expand.
As I understand it, your voting proposal is that each voter gives a number of votes for each candidate, totalling 1. (eg, 0.7 for A, 0.3 for B, or 0.2 for A, 0.3 for B and 0.5 for C). Then, each candidate's totals are added up and the highest wins. If that's not what you're proposing, disregard the rest of this comment.
Suppose there are three candidates, A, B and C. A and C are extremely similar, so nobody has much of a preference between them. 60% of people would like one of them to win, and 40% would rather B won. Under your scheme, as far as I can tell, A and C each get about 30% of the vote each, and B 40%, so B wins. But if C wasn't standing, then A would get 60% and win against B's 40%.
Wikipedia defines "independence of irrelevant alternatives" in the context of Arrow's theorem as follows:
Arrow's IIA requires that whenever a pair of alternatives is ranked the same way in two preference profiles (over the same choice set), then the aggregation rule must order these two alternatives identically across the two profiles.
Also see the subsequent notes on that page about changing the choice set.
In your scenario the choice set changes, and as a consequence many people change their allocation for A. It seems you want something much stronger than independence of irrelevant alternatives. You want a system where removing a candidate and then allowing all voters to adjust their behavior strategically (both of which are disallowed under Arrow's IIA) doesn't change the outcome.
Of course I may be wrong here and in fact I consider myself likely to be wrong because this is a new topic to me, so feel free to correct.
The reason you're seeing these multiple definitions of IIA is because with the appropriate setup, they're equivalent. To be specific:
Let's say we have a finite set of candidates C and a set V of voters. (The set of voters will remain fixed throughout.) Then we can define a (type 1) voting system for C to be a function taking (maps from V to linear orders on C) and returning a linear order on C. With this definition, the natural notion of IIA is the one you describe above.
(Note: Obviously, "type 1", "type 2", "type 3" are all ad-hoc terminology.)
Now we could define a type 2 voting system for a (potentially infinite) set of candidates C to be a family of type 1 voting systems, one for each finite subset of C. Then you have a natural notion of IIA for type 2 voting systems, namely, restricting from one subset of C to a smaller subset shouldn't change the induced order on this smaller subset.
Finally we can consider type 3 voting systems for C, which we will define to be a family of voting systems, one for each finite subset of C, but these all just return single winners, not whole linear orders. The natural notion of IIA for this sort of voting system is the one Khoth describes.
It's then trivial that every type 2 voting system induces a type 1 and a type 3 voting system, and if the type 2 system satisfies its IIA then so do the induced systems. What is less obvious but still not too hard is that if a type 1 or type 3 system satisfies its appropriate notion of IIA, then in fact it must come from an IIA-satisfying type 2 system. (Going from type 1 to type 2 is obvious; to go from type 3 to one of the other types, you run the election, put the winner in 1st, remove him, run again, put the new winner in 2nd, etc.)
So on a finite set of candidates all 3 notions are equivalent and on infinite set of candidates the 2 notions that make sense are equivalent.
I don't have a reference on hand, which is why I don't know if there's standard terminology for this; this is just something I worked out some time ago when trying to figure out why I'd seen IIA defined differently in different places. :)
Ah, it seems like there are multiple definitions for the thing. I'd thought the relevant one was (from the same wikipedia page):
There are other requirements that go by the name of "IIA". One such requirement is as follows: If A is preferred to B out of the choice set {A,B}, then introducing a third alternative X, thus expanding the choice set to {A,B,X}, must not make B preferable to A. In other words, preferences for A or B should not be changed by the inclusion of X, i.e., X is irrelevant to the choice between A and B. This formulation appears in bargaining theory, theories of individual choice, and voting theory. Some theorists find it too strict an axiom; experiments by Amos Tversky, Daniel Kahneman, and others have shown that human behavior rarely adheres to this axiom.
In any case, whether Arrow meant this one or not, it's still something that most people (including me) would think desirable for a voting system to have. I think Arrow's Theorem (and IIA as he has it) is defined in terms of mapping from everyone's complete ordering of preferences to a winner. If your original objection was that an ordering of preferences isn't the proper place to start, you'll also have to change your definition of IIA to fit your new probabilistic starting point.
Yeah, I gave a version of IIA in a previous comment, and I think it's a pretty faithful translation of Arrow's IIA to my formalism. Do you think some other translation would be better?
I think your "tweaking" is too restrictive. Your version forces the allocations to A and B to be unchanged, whereas I think a more accurate translation would be that the ordering doesn't change (or perhaps that the new allocations to A and B are in the same proportion as the old allocations). Those translations produce versions which are broken by your proposed voting system.
ETA: I think we (or at least I) am at risk of falling into the trap of arguing over definitions. Any way of defining IIA needs to be accompanied by a reason why anyone should care about that definition. So, a rough explanation of my position:
The reason we care about Arrow's Theorem is that it basically says "any voting system will have some undesirable properties"
The reason IIA is desirable is that it's a formalisation of the notion that candidates who don't win can't act as "spoilers" that change which candidate does win.
I suspect that by using your probability scheme, even if you can get around the specific definitions of undesirable properties that Arrow used, any voting system based on it will still have analogous bad properties.
In particular, the voting system you propose, third(or more)-party candidates can act as spoilers.
ETA2: Add formatting, and note that my first ETA would likely have been a bit different had I seen your reply first.
On rereading, you're right that my translation was overly strict, and it's obvious that the more lenient translations immediately fail. Thanks.
I googled some more and found a very nice discussion of this topic here on LW: Arrow's Theorem is a Lie. Tommccabe's idea, a reinvention of range voting, is better than mine by pretty much all criteria.
ETA: the rationale for Arrow's IIA still seems different from what you say, because it doesn't allow changing the set of candidates. I'm not sure how to express the rationale for Arrow's IIA so it carries over to other settings.
Thanks for the links, I hadn't come across range voting before.
Like pretty much every voting system ever, it still allows for tactical voting (You naturally give your preferred candidate the highest possible score, but the optimal scores to give for the other depends on how other people are voting). It makes me wonder if that's a thing that voting systems can't get rid of (well, apart from degenerate things like the "dictator" voting scheme).
How about a system that picks a voter at random and uses their choice? This way there's no incentive for tactical voting. But it still violates your strengthened version of IIA because a candidate can steal votes from another.
I forgot to mention the most important fact in my opinion - approval voting, like FPTP, doesn't satisfy the Condorcet loser criterion. In other words there are times when it can actually make the least-popular candidate win. AV can't do that.
I only have knowledge of American politics, but it looks to me like the main benefit of AV is that it would reduce the problem of "spoilers". A spoiler is when 3 candidates run for an office, and 1 of them has similar views to another but only gets a small portion of the vote. Then votes for the minor candidate actually work in favor of the major candidate who agrees with ver least, and thus is not competing with ver for votes. This, as you can see, directly thwarts the preferences of a small portion of voters. It also tends to thwart the preferences of a majority, because American elections are nearly always withing 1-3 percentage points of a tie. The AV system would let people cast symbolic votes for a minor third party, and put a major party as their second choice.
One voting system may be better than another in best representing the desires of a random voter. It doesn't follow that it's better in choosing your personal desires.
I don't know anything about UK politics, but I think you're missing an analysis of whether the switch would be beneficial to you and your political preferences. Although it might be best not to enter such a mindkiller discussion on LW.
Which is why I didn't. Not only would it be a mindkiller result in itself, but the evidence is sparse and very easy to interpret in multiple opposing directions. For the record, I think a yes vote would give a slight advantage to the party I support, and anyone who wants to can find out which party that is in a few seconds, but I would support a yes vote even if it would disadvantage the party I support because I think that long-term my own goals are furthered by having a more democratic society.
In my constituency, for example, last time there were eight candidates. Assuming I used all my preferences (and I would, to ensure the Christian Party were firmly at the bottom) that would give me 8! different possible rankings - roughly sixteen bits of information I could put into the system, rather than one.
A nitpick - but a vote for one of 8 candidates usually carries around 3 bits of information.
I'll be voting Yes but...
Having voters write more on the ballot paper increases the information about what people want that gets put into the system, but it doesn't guarantee that the information will be turned into government policy.
At the moment, small parties can influence policy by having larger parties adopt their best (worst?) ideas in order to avoid having votes drained off them. Under AV, that won't work any more, as small parties would no longer deny votes to their supporters' second choices, and they may stay small for reasons like voting for them being seen to be weird, or because they're single-issue, or whatever.
Thus, AV could possibly result in there being less representation of minority views than currently. Whether things would actually work out this way, and whether it would be a good or a bad thing, I don't know.
It's certainly possible. However, I think that large parties will still adopt smaller parties' best ideas in order to attract preferences of their voters. Where now, say, Labour might bring in an environmental policy of the Greens in order to attract Green voters, under AV they might bring the same policy in so when the Greens get knocked out, their voters will have given Labour a high preference.
That's what I'm hoping.
The existing method works for any small parties, but the method you describe only works for small parties with some kind of cross-party appeal but not for extreme splinters off major parties. That's probably a good thing.
Even if I were to grant your axiomatic assumptions, I seriously question the quality of all those bits voters will be pumping into the process.
Even when voters are presented with a simplified choice of one of two pre-specified coalitions, the quality of that one bit worth of information is highly questionable. Are we really to believe that for any but a tiny minority of voters, we can extract meaningful information from whom they ranked 6th versus 7th?
Alternative Voting, also known as instant runoff voting, produces results very similar to first past the post, while introducing massive headaches. You want range voting or approval voting instead.
IRV leads to 2-party domination
There are three IRV countries: Ireland (mandated in their 1937 constitution), Australia (adopted STV in the early 1900s, but in 1949 added "reweighting" to STV in their multi-winner elections, a change which does not matter for us since we are only considering single-winner elections - Australia and Ireland have both kinds of elections), and Malta. (Later note: a recent addition is Fiji, but it unfortunately then got subtracted due to a 2006 coup.)
All three became 2-party dominated in their IRV seats. And this is despite the fact that in addition to IRV single-winner elections, they all also have multi-winner STV "proportional representation" (PR) elections, and they are parliamentary rather than presidential. Both of these two factors mitigate toward having more than 2 parties (the parliamentary countries with PR essentially all have many more than 2 vibrant political parties). But despite those multiparty-genic factors, the effect of IRV in these countries has been enough to drag them back down to 2-party domination status! So given that, you can bet your bottom dollar that the USA, were it to adopt IRV but still to remain presidential and without multiwinner PR elections (i.e. wholy with single-winner elections), will definitely stay 2-party dominated.
I strongly urge anyone who cares about voting systems to poke around this site for a while, it's very well-written.
Also, it is extraordinarily impolite to post a comment containing a link, then, after a reply has been posted, edit the link to point somewhere different. I don't currently have enough karma to downvote, but if I did I would definitely downvote such a flagrant breach of basic etiquette.
For the record, PlaidX's original link was to http://www.rangevoting.org/IRVcs.html . The link now points to http://www.rangevoting.org/TarrIrv.html . And the argument there is a specious one, in that the situation described only works if the "best" voters know how everyone else is going to vote. Which they don't.
Yes, so in a highly-artificial scenario, AV can produce a result no worse than the same result under FPTP. Both range voting and approval voting can lead to the single least-popular candidate getting in. See http://archive.fairvote.org/?page=1920
And more to the point, neither of those are on the ballot paper. AV is.
Hi Andrew,
In the link you sent, the person who has evaluated Range voting has evaluated a system based on totaling and not averaging based range voting with a reasonable quorum as it is described in rangevoting.org.
There are a number of reasons that averaging is preferable to totaling especially in sceanrios with incomplete information.
I'm pro-av, but the rational anti-argument would be is that you are finding not the most popular candidate, but the least hated. I actually think this is fine, but some people extremely dislike the notion of ending up with a compromise candidate no-one really wanted.
Also, If we have members A B and C, A with 35% support, B with 30%, C with 30% and D with 5%, then we could end up with D's voters having a very strong effect on who gets elected. D gets eliminated first, and then their votes get redistributed. Depending on if they like B or C more then B or C might get eliminated, leaving us with A or B. D's voters don't decide who wins, but they make sure who loses- it might be that the voters for B would have given their support to C if it had gone the other way, so C could have stood a real chance of winning if it wasn't for D's voters.
So in many ways this run off can lead to what feel like undemocractic results, although I still believe they are superior to the flawed FPTP
I see ending up with the 'least hated' candidate as a benefit, not a downside. And while "C could have stood a real chance of winning if it wasn't for D's voters", again, that's not a downside - minority votes should count too...
I agree with your first point, but not necessarily your second. To make this clearer, lets imagine that:
D voters like C and hate A
C voters hate A
B voters hate C
we saw
A 35%, B 31%, C 29% and D 5%.
D gets eliminated, and they all love C, leaving us with
A 35% B 31% C 34%.
B voters hate C, so they've all voted A, leaving us with
A 66% C 34%,
D voters sigh, and accept A's landslide victory
If instead D chooses to vote B we get
A 35% B 36% C 29%
which then reduces to
A 35% B 65%
and D voters can't grumble. Now this is a tiny bit artificial, but it shows that minority votes can be disproportionality powerful in weird ways: D voters in this example are much better off NOT going with their guts and voting C if they really don't want A to get into power, especially if they know B voters hate C.
One of the nasty things about this is that while in FPTP tactical voting is fairly easy (look at which party opposing your most hated candidate got the most votes last election, and vote for them), in AV its actually really hard to work out where everyones preferences will go.
That said, I still really like AV. One of my main reasons for liking it is that it has the potential to reflect what voters actually think. Theres certainly no waste of a first preference here, which means you truly can vote for your favourite party, which could lead to surprising results.
"One of the nasty things about this is that while in FPTP tactical voting is fairly easy (look at which party opposing your most hated candidate got the most votes last election, and vote for them), in AV its actually really hard to work out where everyones preferences will go."
That's actually a good thing. Tactical voting not only leads to the 'wasted votes' you describe, but extreme unhappiness in other ways. A lot of people who claim to have voted Lib Dem to 'keep the Tories out' but to have preferred Labour are now very, very angry at the Lib Dems for joining a coalition with the Tories. Under AV, those people's MPs (assuming they're telling the truth) would know that the mandate they had wasn't a 'Lib Dem' mandate or a personal one, but an 'anti-Tory' one, because they'd only have got in through Labour voters' second preferences. This means that if (as many people who claim to be disgruntled ex-Lib Dem supporters claim) most Lib Dem voters are 'really' 'anti-Tory' voters, the Lib Dems would have had a lot more incentive to make a deal with Labour, rather than with the Tories. And of course if they weren't 'really' 'anti-Tory' that would have been reflected too.
It sounds like it comes down to getting to express your preference while still not risking "wasting" your vote. I think getting clear preferences registered and not getting the interference from tactical voting speculations is a real benefit even if there are cases with surprising outcomes.
At this point I suggest asking "what's it for?" Then ask "what could it be useful for?"
One answer that occurs to me for the second question is merely to change the system to unclog it a bit. One argument for "Yes" is that it will shake up currently safe seats. But I'm from Australia, which has an AV-like system, and the safe seat problem there is every bit as bad as it is in the UK.
As such, I suggest it may be explicitly beneficial just to change the system slightly every now and then, to dislodge complacency.
(Obvious danger: breaking it.)
I must admit I'm not sure how to make this a more robust hypothesis, let alone a quantifiable one ...
One big advantage would be solving the whole "X can't win here! Only Y can keep Z out!" problem, and allowing people to express their actual preference rather than one based on a best guess as to what other people would do. Even if that leaves us with safe seats, they will be safe because a majority of the people in the constituency genuinely want them to be. At the moment, there are some safe seats (e.g. Hazel Blears' seat in Salford) where a majority of the voters want their MP out, and the MP is genuinely horribly unpopular, but there's no way for those voters to co-ordinate between themselves and settle on the most likely alternative to kick them out.
I'm speaking in more meta terms than the particular advantages of this as a proposed system for the indefinite future. Would kicking the system every few decades actually be a very good idea?
It could be - except that at some point you have to move from a 'better' system to a 'worse' one. At which point, people complain - rightly - that they are getting a worse democracy because of some meta-rule. Possibly one option, if we're talking about that kind of radical change, would be for every election to also have a referendum on how the next election would be held - with four or five options each time (say FPTP, STV, AV, AMS, AV+ or something). Each time, the least popular option from last time will be removed from the ballot and replaced with a different system. (Of course then you get into a meta-meta argument about how to count the referendum votes...)
How does the system work in practice in Australia? Do candidates have safe seats because they represent popular views, or are there other factors that stop them from being challenged?
What Andrew said. But basically, safe seats happen when a system is (IMO) too stable, such that the election is decided by marginal seats.
But this is getting towards my own political opinions, which somehow are boring even me to type on LW ;-)
One of the differences between the Australian system and the proposed UK system is they have compulsory voting and compulsory ranking of all candidates, neither of which would be in play in the UK. This has lead to 'above the line' voting, where parties register what they want their supporters to put as their preferences, and then you can just mark a box for that party and you get assigned that party's registered preferences. This gets rid of many of the advantages of AV (though not all, as people are free to express whatever preferences they want - it's just that 95% of them don't) in favour of backroom deals between parties for preference swaps.
Yes, at the end only one candidate is selected, but the information isn't 'thrown away' - the MP now knows, rather than just "52% of people in the constituency voted for me", "27% of people voted for me as their first preference, with the Greens as their second preference, 25% voted for the Greens first and me second, and nobody at all voted for the Tories first and me second, or me second and the Tories first. That means that I'd better pay attention to my environmental policies, which I share with the Green, and maybe not so much my economic policies, which I share with the Tory".
Or, to look at it another way, the system does throw away all but one bit of information, but the information going into the system is used to tell it which bits to throw away.
Well, we already have lots of polls.
I know 'Politics is the mind-killer' and I'm prepared for downvotes here, but thought this would be worth pointing out.
In the UK at the moment we're preparing for a referendum, on May 5, on whether to switch our voting system for General Elections from First Past The Post (FPTP) to the Alternative Vote (AV). I see this not as a question of politics (the fact that it crosses normal party lines tends to suggest I'm right) but as a question of information theory and cybernetics. Once it's seen in that light, the answer becomes obvious.
Unfortunately, the only real coverage this has received in the media has been along group identity lines. Both sides claim the Nazis would benefit from a vote for the other side, and other than that the No campaign's line has been pretty much "There's a black man in this leaflet but not this other one, therefore the Yes campaign are racist!" or "Nick Clegg likes AV and you don't like Nick Clegg, therefore you don't like AV!"
Meanwhile the Yes campaign has been little better, its main campaign consisting of "MPs don't like AV and you don't like MPs, so vote Yes!" and "Stephen Fry likes AV, and you like Stephen Fry, so vote Yes!"
It would be quite understandable, with debate like that, if the average British LessWronger were to think that the matter was just a matter of normal mammalian status politics, on a par with the riots last year over whether to call something a 'graduate tax' or 'tuition fees'. But in this case, there is a substantial difference, and an obvious rational choice.
Assuming, for the moment, that we're agreed that representative democracy of some form is a reasonable system of government, one of the main advantages of that system is that it has to be somewhat responsive to the citizenry - voters put information into the system at election time, and that information determines the makeup of the government.
Assuming we think that a good thing, we want to maximise the amount of information each voter can put into the system. The more information put in, the more accurately the government can respond to the will of the people.
Now, with First Past The Post, the system is that in each constituency, the candidate with the largest number of votes gets elected, and all the candidate cares about is his/her majority over the candidate with the next-largest number of votes. This means that in all but a very small number of cases, the only votes that 'count' in any important sense are those for the first and second-placed candidate. That means each voter gets to influence the government at a bitrate of one bit every five years. Not great.
With AV, on the other hand, voters rank candidates, and then the candidate with the lowest number of first preferences gets knocked out and their votes redistributed to the voters' second preferences. This process is repeated until one candidate has over 50% of expressed preferences.
This *vastly* increases your ability to put information into the system. In my constituency, for example, last time there were eight candidates. Assuming I used all my preferences (and I would, to ensure the Christian Party were firmly at the bottom) that would give me 8! different possible rankings - roughly sixteen bits of information I could put into the system, rather than one.
Clearly, the rational thing to do in this case is to vote yes, to increase the effectiveness of the democratic system. Unless I'm missing something, in which case I'm sure the comments will say...