RIP Peter Strawson

Peter Strawson died today. Obituaries in the usual major papers...

I don't think I've ever seen him, or know much of his work; but his son Galen interviewed me for admission to Jesus.

Wigan 0-1 Liverpool

I didn't see this game, since I was away in Warwick, and couldn't be bothered to stay up until the end of Match of the Day for a 1-0 win over Wigan, but it's good to see us pull out three points again after a troublesome one point from four games. Maybe it helped that Wigan didn't have any strikers, but we've had our problems there too - Pongolle remains our only striker to have scored this year.

Hopefully Gerrard (who played) and Crouch (who didn't) will be fit for Arsenal on Tuesday. That tie, followed by Man Utd in the FA Cup and Benfica in the CL, will go a long way to shaping the success of our season.

Some other results of note were Middlesbrough's shock 3-0 win over Chelsea (whose next game is vs Colchester United...), and Arsenal's late draw with Bolton - in which I saw Lehmann push a Bolton player over but not (like Reina) get punished at all...

Warwick

Today I'm attending the Eighth Annual Graduate Conference in Political Theory at the University of Warwick (which is, confusingly, in Coventry). Looks a pretty good programme, with plenty of Oxford people - including me giving my first paper outside Oxford.

You Spin Me Round

I went to see Alaistair Campbell give a talk tonight. Sadly, Chatham House rules apply, so I can't go into details - though actually apparently all that's prohibited is me attributing anything to him by name - so if someone in Oxford recently heard anything from a 'source close to government' here's a clue...

Happy Birthday Julia

Happy birthday Julia, the scary mid-20s...

Going to the Gardener's Arms later to celebrate with people from the department, Nuffield and other random places to celebrate (but will be suitable restrained since I'm teaching tomorrow)

Charlton 2-0 Liverpool

Another disappointing defeat, and worryingly Liverpool have only taken one point from their last four games. Defeats to Man Utd and Chelsea hurt, but are understandable, to Charlton is more painful... Unfortunately we've lost form at the worst time. Even when we were drawing games at the start of the season, and about 12th in the table, I was feeling more optimistic than now.

Even neutral reports suggest the game turned on the controversial penalty decision that gave Charlton the lead against the run of play. I think this is one of our problems. Our strikers simply aren't putting away goals. Consequently as long as we don't concede, we capable of standing firm for at least a draw, and often nicking a win. If we go behind, however, we struggle. We don't have enough firepower to get back into the match, and if forced to chase it, tend to expose ourselves at the back, thus conceding more.

I can only hope Robbie's soon back to fitness and goal-scoring form.

Reading Group (HT 06 wk4)

For this week's reading group we decided to meet at the Angel & Greyhound (on St Clements, close to Magdalen roundabout) at the usual time of 8:30 Wednesday.

The chosen reading was Barbara Fried's 'Left Libertarianism: A Review Essay' Philosophy & Public Affairs 32:1 (2004) pp.66-91, the reply in P&PA 33:2 (2005) pp.201-15 and her rejoinder to that pp.216-22 of the same volume.

Memorable quotes:

OK: We're getting into utilitarianism for lions.

KO: Stop throwing long words at me.
SW: I'm just making up words now.

KW: It's not to do with Nozick, it's about a hypothetical.

SW: I treat my [one year old] daughter as an object.

KW: Not everything that doesn't exist is weird.

KW: Death is bad, it just isn't painful.

OK: I think it's worth... Well, not worth, but interesting to distinguish...

KO: I think there's been a massive increase in pedantic comments.
Me: We're philosophers!

OK/KW/KO: Every week we end up discussing pro tanto reasons.

KO: I didn't mean to get into paedophilia.

Women's Ambition

I'm wary of stepping too far into feminist territory here, especially after last week's post, but here's something that perhaps goes some way to vindicating what I claimed there: that women would be better served by society valuing 'women's [i.e. domestic] work' rather than by giving them equal opportunity to compete for traditionally male jobs.

Anyway, what first caught my attention was seeing this book: It Takes a Candidate : Why Women Don't Run for Office. I haven't read it, so I don't yet know the answer. I'd predict a mixture of reasons, from family responsibility and socialisation to a distaste for the world of politics and all the butt-kissing it seems to take to get ahead in any career (academia included).

Now, I suppose the question is whether women's choices should be respected, or whether this is a 'contented slave' kind of case - one in which through adaptive preferences they're happy with what they've got, even though they shouldn't be, and where Rousseau's paradoxical comment 'forced to be free' makes some sense (though perhaps it'd still be better expressed 'forced to do something more worthwhile', without misdescribing perfectionism as freedom, but let's not get into that now...)

The other thing I saw, just now in fact, actually comes from the press release to Pink's new single 'Stupid Girls', and it's quite worrying:

In a recent survey published by The Sunday Times, girls aged between 15 and 19 were asked which careers they wished to pursue. 63% said glamour modelling and
25% lap dancing in comparison to 4% saying lawyer and 3% doctor – a shocking upshot of the superficial cult status of today’s airhead celebrity.

I haven't seen this survey, perhaps I should look it up, but it suggests one big reason why women are still under-represented it top professions - and also explains the glut of useless celebrity/'reality' crap on our TVs.

Admittedly, I'd be surprised if a lot of boys didn't want to be footballers or rock stars or something, but at least they do something with their lives. I assume a lot of girls would rather just be rich and idle, like Paris Hilton or Tara Palmer-Tomkinson. The traditional expectation to be the breadwinner generally forces boys to give up unrealistic pipedreams and either get a decent education or start a career early (or perhaps turn to crime, etc). I'm going to be controversial here, but perhaps too many girls are still in a 19th century mindset in which they simply concentrate on some form of self-improvement (e.g. education) and other passtimes, while waiting for a man who can keep them in a life of luxury they've somehow come to expect from too much escapist TV...

Obviously that's a simple stereotype, but the original point is maybe the reason there aren't many women in so called 'top' positions in society is that they don't want to be there. The question we should be asking is whether that's a problem or not.

Philosopher's Humour (HT06 pt 1)

Time for an over-due return of those little snippets that make seminars worthwhile. Here’s today’s (as ever, just the gists).

Ethics 06/02/06

GAC: No I’m talking about real dogs. A real dog wouldn’t say its meal is tasty, because real dogs can’t say anything.

Presenter: Another Dr Cohen...
GAC: I'm not actually a doctor
Presenter: Well, you're obviously very distinguished nonetheless, so we won't hold that against you.

Nuffield Political Theory Seminar 06/02/06

[Discussing whether having a right you can’t exercise can make you better off]
DM: I hereby grant you the right to float in the air unsupported
AW: Were you denying me the right before?

[On proposals concerning legitimate group ownership of land]
AP: That’s wouldn’t work for Jerusalem
RS: Nothing would work for Jerusalem

Moral Philosophy Seminar 06/02/06

[Introducing his paper on Bernard Williams]
JS: Although I will disagree with most of what he [Williams] says I’m sure I’m probably wrong…

SuperBowl XL

That doesn’t mean eXtra Large, but 40. I’m not exactly an American football fan. I watched about half the Superbowl two years ago in college, and this time again a big bunch of us decided to pile round a friend’s for beer, Doritos, pretzels and watching big American guys beat the crap out of each other.

The atmosphere was greatly improved by some inspired music thanks to Nick's i-Pod, including Led Zep's 'Immigrant Song' and Chumbawumba's 'Tubthumping'. Extra comedy value for playing the wrong AC/DC song too... On which, Ed's comment "Not having cheerleaders is sexist. What are the women supposed to do?" is also worthy of mention. (We had our own Pittsburgh cheerleaders in Lisa and Sanne, however)

Most of us only declared allegiances a day or two before the match, so weren’t too bothered. I was for the Seattle Seahawks, who lost. Unfortunately pretty much all the dodgy refereeing decisions went against them – as revealed here. I can’t be bothered to go through them all, but Seattle had a touchdown denied, and Pittsburgh were then given a debateable one – so what could’ve been 10-0 was actually 3-7.

I have to say, I seemed to have a pretty good grasp of what was going on by the end of the game. I was even able to have a conversation about it later with an American. Wish I hadn’t stayed up until 3am for the result though…

Chelsea 2-0 Liverpool

Well, another big Liverpool vs Chelsea game and another defeat. In fact, it seems we lose all the domestic matches, even if we can hold them in European competition – don’t know why that is.

What was most annoying was the general manner of defeat. We seem to have run out of steam a bit, and it’s not surprising how tired many players look given the long season we’ve already had (with pre-season CL qualifiers and a trip to Japan) – unfortunately it’s come at the crunch time of the season, with important matches against our main league rivals, Man Utd in the FA Cup and Benfica in the CL all coming up.

In fact, their opening goal came against the run of play. Unfortunately once we were behind, our heads went down. Maybe it’s the tiredness, but we gave up too early, rather than continuing to the 92nd minute… After that, neither our defence nor attack looked good.

The main talking point is probably Reina’s red card, for a moment of madness towards the end, which certainly didn’t help our cause. Haven’t seen the incident, so I can’t really comment in detail – Reina shouldn’t have been raising his hand, but by all accounts Robben went down like a sack of bricks.

UPDATE: I suspect whoever wrote this on the Liverpool website:

Former Liverpool captain Jamie Redknapp has condoned the 'play-acting' actions of Arjen Robben and sympathised with Pepe Reina over his controversial sending off at Stamford Bridge on Sunday.

Doesn't know their 'condoned' from their 'condemned'.

Cartoons

It seems everyone wants to add their two pence worth to the furore over these offensive cartoons (for example, here and here). I haven't got much to add to these eminently sensible comments.

Free speech means the newspapers can say what they like. It may be wrong to say something offensive, but it's still your right. Some people I saw interviewed on the news suggested free speech must always be within seemingly quite narrow limits of not offending people. Since some people will be offended by almost anything - and you can't please all the people all the time (to adapt a phrase) - this seems to me like saying 'you have complete freedom of movement, provided you don't leave your house'. The importance of free speech means we must be free to offend people who don't share our views (although appealing to something like the doctrine of double effect, I'd say offence should be a tolerable side-effect but not the intention).

Of course, anyone offended has the right to express this - that's their freedom of speech - and they can condemn or even boycott the newspapers in question (as many Liverpool fans still boycott The Sun, for example). Needless to say, burning embassies does not fall within the scope of reasonable protest.

(For an example of relatively benign - if in my opinion slightly prudish - newspaper cartoon editing/censorship, see here)

UPDATE: Further thoughts from Index on Censorship, here and here.

Blogger Meet Update

February 21st (Tuesday of 6th week). 8pm. Turf. (See here)

Women Have It All

After spending most of tonight glued to Channel 4 - largely from inertia, though new comedy The IT Crowd was a big improvement on Celebrity Big Brother (which I refused to watch) - I felt moved to comment on Amanda Platell's slot on female emancipation:

30 Minutes Political commentator Amanda Platell suggests feminism has offered today's women an unrealistic dream of independence and career success, threatening their chance for real happiness with a husband and children. She considers the impact second-wave feminists had on society in the 1960s and 1970s, and reflects on the personal choices she herself made.

(From Guardian TV guide)

The general line was that feminists have shot themselves in the foot, by demanding the right to work modern women now have to combine this with raising families, and get the bad of both worlds - and that, in effect, may would've been happier in a simpler age as home-makers.

In fact, I'm sympathetic to such general arguments, believing that women would've done better to promote the valuation of the domestic sphere, rather than abandoning it for a right to work. After all, what's so great about being a wage slave? Different but equal - with rights for either sex to take on the non-traditional opposite gender role - is, I think, probably the way to go here.

The programme, however, was full of far too much over-simplification and proceeded to state a succession of banal truths in a one-sided fashion. For example 'women now want families and work, but feel they can't have it all'. True, but men can't have it all either. Sure a stay at home wife allows you to combine a career with having children, but not spending quality time with them. Similarly, the observation that women - caught by this schizophrenia - no longer know what will make them happy. But do we know what makes anyone happy? No. The problems raised - superficially - in the programme aren't those of women, they're problems of everyone (men and women) in modern society.

Liverpool 1-1 Birmingham

I was rather disappointed to get home and find this result. I'd been in the pub - where the Arsenal match was being shown - but after seeing Alonso's name flash up late on, I hoped he'd put the game safe. As it happened, when I got home I discovered he'd conceded a late own goal. Particularly frustrating to draw at home to a team like Birmingham, especially after they played an hour with ten men... On the positive side, Birmingham are a bit of a bogey team for us. Last season they beat us twice, this season two draws marks a significant improvement - and with Man Utd, Arsenal and Spurs all losing (and Chelsea also only drawing) it's a point gained on our main rivals, even if three would've been better. Too bad Robbie's overhead kick was ruled off-side, as it would have been a great comeback goal.

Arrow: Criticism and Defence

A while ago I promised a reply to John Lawrence's Criticisms of Arrow. Here it is, point-by-point. (Hope you don't mind me copying them John - if you do leave a comment and I'll edit your bit out)

1) Arrow doesn’t allow ties. Example: For alternatives a, b and c, the only acceptable social choice for Arrow is one of the following: abc, acb, bac, bca, cab, cba. A tie would be of the form {abc, bca} where the parentheses indicate that the two social rankings abc and bca are tied.

I don’t think Arrow disallows ties. See below, but ‘indifference’ counts as a decision. Of course, trying to choose between policies x and y, knowing society is indifferent between them doesn’t much help. Perhaps we can resolve indifference by tossing a coin, as many have suggested for tied elections. Technically that doesn’t fit Arrow’s general project, as it only breaks deadlock, it doesn’t produce a social ranking – but then, I think he’s wrong to require such anyway.

2) Arrow assumes that a tie is the same as an indifference. Let’s assume 2 alternatives: x and y. Also that half of the individuals in society prefer x to y – xPiy for half – and half the individuals prefer y to x – yPix. Pi represents the preference ordering of the ith individual. Arrow would say that society is indifferent between the 2 alternatives – xIy. However, society is not indifferent between the 2 alternatives. Society is evenly divided between the 2 alternatives. Half prefer x to y and, let us assume, very passionately. Half prefer y to x and, let us assume, equally as passionately. Society would be indifferent if every individual was indifferent between the 2 alternatives.

Arrow doesn’t just ‘assume’ this. There’s an argument p.50 ff. intended to establish that if x and y tie, yet we take one to be preferred, we get inconsistent results. (The argument was too technical to follow easily, let alone recall or reproduce here, but believe me there is one)

Of course, this doesn’t quite answer the challenge, as the criticism isn’t that either x or y should be preferred – it’s that there’s a fourth possibility: xPy, yPx, xIy and xTy where the T relation stands for ‘ties with’.

I think there is something to this, but note there’s now a problem. Jonathan says “Society would be indifferent if every individual was indifferent between the 2 alternatives” but it isn’t clear if this is merely sufficient or also necessary. What if 99% were indifferent and the 1% evenly split each way? Surely that’s also social indifference rather than a tie. What if the 1% mostly support x? Is the social choice now xPy or xIy? The problem is that introducing this extra possibility means we’re now longer dealing with a binary x or y choice, because tying is (unlike indifference) a third option.

3) According to Arrow the only information an individual may specify is pairwise binary comparisons. Any other information is irrelevant. However, there is no reason why an individual shouldn’t specify as much information as possible. For instance, if x, y and z are the alternatives, Arrow would say that the only relevant information is in comparing x to y, x to z and y to z. It is easy to imagine a grid with values from 1 to 100, for example. An individual could place x, y and z on this grid in any position. This would convey more information than binary comparisons Why shouldn’t each individual have unlimited freedom of expression?

If you can’t compare interpersonal utility, the problem is this ‘extra information’ is meaningless. I may rank a, b and c as 1, 50 and 100 and you may rank them 1, 99, 100, but this doesn’t mean anything. We can’t conclude I prefer b more than you do, so why allow voters to express something that has no meaning?

4) There is no such thing as an irrelevant alternative. The number of alternatives determines the underlying grid. If that grid changes due to the death of one of the candidates, for instance, the individual’s preferences, if he is required to specify them within a grid determined by the number of candidates, may change. Preferences may become indifferences and vice versa.

This is to some extent a fundamental disagreement, too close to premises to resolve, and one where John essentially sides with Borda against Condorcet and Arrow. It doesn’t seem obviously wrong to say all that matters in choice between x and y is the relative ranking of x and y, however. Why compare them to non-option z, particularly in light of the above point that it doesn’t even allow some kind of interpersonal comparison?

The death of a candidate is actually a slightly different case. Arrow himself confuses independence of irrelevant alternatives with contraction consistency, which is related but can be distinguished. Still, suppose you rank aPbIcPd then c dies. It seems natural to suppose the remaining preferences simply carry over – aPbPd – unless some good reason is given why they might change (non-strategically).

5) Since there is no such thing as an irrelevant alternative, one of Arrow’s “rational and ethical” criteria is invalidated. Therefore, his entire analysis is invalidated.

This is rather hasty if 4) hasn’t been sufficiently proven…

6) We don’t know how an individual would vote if one candidate died, for example. If the number of candidates changes, the individuals must be repolled or else some probabilistic assumptions would have to be made about how they would have voted. You can’t just assume that because an individual voted aPbIc, if a dropped out, the individual would still be indifferent between b and c. For example, let us assume that there are 3 candidates, a, b, c and Hitler. A voter might vote aIbIcPHitler with the rationale that any candidate would be preferred to Hitler. Then, if Hitler dropped out, true preferences among a, b and c might emerge.

This rather repeats 4). If there are true preferences between a, b and c, why hsouldn’t they emerge before Hitler’s death? Thus if the individual would want to vote aPbPc without Hitler in the frame, they should want to vote aPbPcPHitler with Hitler, preserving “the rationale that any candidate would be preferred to Hitler”.

7) An individual shouldn’t be prevented or constrained from using his vote in a strategic way. In any rational voting system there is what Arrow calls the “Positive Association of Social and Individual Values.” Therefore, an individual will express preferences based on the candidate set in order to prevent a particular individual from being elected or to help guarantee that another individual will be elected if he feels that strongly about some particular candidate. The individual shouldn’t be required, as Arrow does, to vote consistently when the candidate set changes. For example, let’s assume that the candidate set consists of candidates a, b, c and Jesus. It would be an entirely rational vote to specify (Jesus)PaIbIc. Compared to Jesus, the individual is indifferent among a, b and c. Now let us suppose that Jesus drops out of the race. Then it would be entirely rational for the individual to vote aPbPc. In other words, the voter voted strategically to get Jesus elected and should be allowed to do so. If Jesus is not in the race, the individual’s true preferences among a, b and c emerge. Arrow’s condition, “Independence of Irrelevant Alternatives” is not rational after all.

Again, this criticises 4), but explicitly claiming the individual should be allowed to vote strategically. I’m not sure about that. Sometimes I think strategic voting is defensible, so long as all have the same opportunities to use their votes, it’s up to people how they do so. Certainly no argument for strategic voting is given here, however, so nothing to convince anyone who already believes it’s wrong.

8) “Adopting an informational perspective, then, [Arrow’s theorem] just state[s] that procedures for three or more candidates require more information than just the relative rankings of pairs.” Saari, DG, (1995), Basic Geometry of Voting, Springer-Verlag, Berlin.

I don’t see the point being made here.

9) Rankings have been considered to be cardinal or ordinal where ordinal represents a simple ranking and cardinal allows more information. Cardinal rankings supposedly allow “preference intensity” to be represented. It’s not about preference intensity; it’s about freedom of expression. Let’s add a third type of ranking: digital. An ordinal comparison for 3 candidates can be specified by 3 bits since there are 6 possibilities. If we allow more bits, then more information and relevant information can be gleaned from each individual. Allowing each individual to specify his or her preferences using the same number of bits eliminates the “interpersonal comparisons of utility,” another of Arrow’s bugaboos. There is no preference given to one individual over another because of supposed greater need. Therefore, allowing more than just ordinal information is just as impersonal as allowing only ordinal information.

This claims to be like 3) but without making interpersonal comparisons, however I don’t see what is supposedly expressed. How about another box on the ballot allowing voters to express their favourite flavour of ice cream? Surely that’s also more expression and therefore better (though I don’t see how it should influence the decision in question).

10) Arrow constrains freedom of expression.

See 3) and 9). I don’t think Arrow constrains ‘free expression’ in any troubling sense – he wouldn’t repeal the First amendment, for example – all he restricts is what influences social choice.

11) Arrow confuses ties and indifference in the binary case in which there are 2 alternatives and n voters. See my paper, "Neutrality and the Possibility of Social Choice" He says majority rule when there are only 2 alternatives is the only case where social choice actually works. But according to his analysis, if done correctly, social choice isn’t even possible with 2 alternatives. The key point is that when the number of voters who prefer x to y, N(x,y), equals the number of voters who prefer y to x, N(y,x), you have a tie between the solutions xPy and yPx which I indicate {xPy, yPx}. This is not the same as xIy, x is indifferent to y.

This is basically point 2) repeated. (Again, I suggest tossing a coin to resolve ties).

12) Arrow violates the Principle of Neutrality in his analysis of binary majority rule. The Principle of Neutrality states that each alternative (in this case x and y) must be treated in the same way. No alternative may be given preferential treatment.

How does Arrow violate Neutrality then? Neither x nor y is given preferential treatment (unless ties favour status quo, which is slightly non-neutral). But see 16).

13) In the binary case, Arrow assumes that a tie in the domain of individual votes implies a social indifference. The domain consists of all possible combinations of votes by the individual voters. The range consists of all the possible choices by society as a whole i.e. social choices.

I’m not sure what point is being made here, but since it concerns ties again I suggest it’s much the same as 2) and 11).

14) Arrow states (p. 12, 13 of “Social Choice and Individual Values”): “A strong ordering…is a ranking in which no ties are possible.” WRONG! If n/2 voters prefer y to x and n/2 voters prefer x to y (n being even), this clearly is a tie! This section clearly shows Arrow’s confusion between the concept of a tie and the concept of indifference. He thinks that both xRy and yRx imply a tie. Wrong again. They imply an indifference.

A strong ordering is one where no ties are possible. That’s definitional. If voters are evenly split, you get a tie, but that’s because the result isn’t a strong ordering! As for the tie/indifference distinction, see 2) and 11) – this increasingly seems John’s main, perhaps only, complaint.

15) Arrow’s R notation. On p. 12 of “Social Choice and Individual Values,” Arrow states: “Preference and indifference are relations between alternatives. Instead of working with two relations, it will be slightly more convenient to use a single relation, ‘preferred or indifferent.’ The statement ‘x is preferred or indifferent to y’ will be symbolized by xRy.” Emphasis added. Slightly more convenient? Ridiculous. What voter votes in such a way that they are “preferred or indifferent” between x and y. What would be the meaning? Maybe I prefer x to y or maybe I’m indifferent? I don’t know which? The net result is that the voter is constrained to make choices of this nature when he damn well knows he prefers x to y or he damn well knows he is indifferent between x and y. Heuristically, the R notation is nonsense. If I’m going to list my preferences, I can do so unambiguously using P and I. For example, aPbIcPd would indicate that I prefer a to b, c and d; I’m indifferent between b and c; and I prefer a, b and c to d. See "Arrow's Consideration of Ties and Indifference"

It is nowhere implied that voters don’t know whether xPy or xIy. The R notation is simply a representational device, equivalent to ‘equal to or great than’. It’s true all Rs can be cached out in terms of P and/or I, but perhaps sometimes we don’t know which so to write ‘xPy or xIy’ is more troublesome than simply ‘xRy’. Conversely, nothing is lost by using R notation. We can express xPy by ‘xRy and not yRx’ and xIy by ‘xRy and yRx’ (the ties/indifference problem not withstanding). The R relation allows us to represent everything we want – great than, equal to, and equal-or-great – using a single formula. In that respect, it’s more flexible and economical. Granted it doesn’t seem particularly necessary, but it’s far from absurd, and doesn’t have the implications John tries to draw.

16) Definition 9 (p. 46) The case of two alternatives. “By the method of majority decision is meant the social welfare function in which xRy holds if and only if the number of individuals such that xRiy is at least as great as the number of individuals such that yRix.” This is totally ridiculous. First of all it violates one of Arrow’s five “rational and ethical principles” which all social welfare functions must comply with: the principle of neutrality. When the number of individuals such that xRiy equals the number of individuals such that yRix, why is the solution xRy? Why not yRx which is equally as valid? In fact it is a tie between xRy and yRx, or according to Arrow’s own terminology, when xRy and yRx, then xIy not xRy! But wait, there is more. If half the individuals prefer x to y and half prefer y to x, we have a tie between x and y: {xPy, yPx}. If all the individuals are indifferent between x and y, we have a societal indifference: xIy. These are not the same thing! If more prefer x to y than prefer y to x, we have xPy and vice versa. If some individuals are indifferent between x and y, but more prefer x to y than prefer y to x, we have xPy and vice versa. This pretty well covers all the cases. Arrow is determined to ignore the significance of a tie and to turn a societal indifference into a tie. See "Arrow's Consideration of Ties and Indifference"

This seems to explain what was meant by 12), by repeating and elaborating the claim majority rule is non-neutral. It is, however, mistaken. Jonathan asks why xRy and not yRx. It is also yRx. As states in the previous section, xRy and yRx can hold together and imply xIy. Thus Jonathan either has no point, or it’s merely the ties/indifference thing again (see 2), 11), etc).

17) Arrow defines an indifference as a tie.

Yup, see comments on 2), 11) and 16).

It seems John’s only serious criticism is to treating ties and indifference as equivalent. It’s true, this does worry me as well. I wondered why, for May too, a split 4/993/3 between xPy, xIy and yPx results in a social choice xPy. It hardly seems intuitive but, as I said above, to introduce indifference as if it was a third option takes us away from the binary choices being dealt with.

There does seem to be a difference between everyone’s indifference and an even split between x and y – though in both cases I might suggest tossing a coin for decision-making, albeit for slightly different reasons (in the first simply to make a decision, as an individual might do in ‘Buridan’s ass’ like cases; in the second to be fair to everyone, i.e. give them an equal chance of getting what they want).

I don’t know what else to say about this issue. There’s certainly room for many whole papers on the topic. I think, however, it’s all these criticisms boil down to. (Plus some unsubstantiated assertions of rights to ‘free expression’ and ‘strategic voting’) – So it’s far from clear to me that Arrow is refuted, and the presentation of ‘17 criticisms’ significantly overstates the objection to make the case look stronger than it is.

Fire Alarms and Stop Outs

We were rather rudely awakened by a fire drill at 2:45am this morning.

Not that this bothered my flatmate Pavel, of course, since he didn't get home until 9am...

Portsmouth 1-2 Liverpool (FA Cup)

Nice to see Liverpool on the BBC again. Well done Lawro and Hansen!

Granted Pompey away wasn’t the toughest draw possible, but it was bound to be tricky too. With that in mind, I was pleased how we handled the first half, looking fairly comfortably in control for much of it, but without creating many real chances. It looked rather like a tie against lower league opposition – as if we were confident we’d win and consequently lacking any urgency.

The breakthrough came from a very well-taken Gerrard penalty. Probably since Murphy’s departure we’ve lacked a regular penalty taker who inspires confidence, with both Stevie and Cisse sometimes good sometimes shocking. I’d quite like to see Kewell or Fowler given a chance, but with neither on the pitch, it was Gerrard who staked his claim.

I thought the award – handball against St? for handball as Primus cleared – was harsh. Mind you, Pompey fans can’t complain too much – in the first half at least three of their players made bad tackles, any of which could have been red-carded, not to mention Vignal elbowing Stevie in the ear…

Riise doubled the lead soon after with a trademark left-foot thunderbolt on the break. Sadly the second half wasn’t to be more of the same. Pompey switched to a 3-5-2 which gave Liverpool far more problems, and even Cisse’s pace never looked like troubling them at the back. The arrival of Crouch – given a hostile reception as a former Saint – did at least improve our hold-up play, but I’d have loved to have seen Sinama Pongolle again after his effect against Luton. Most disappointing was probably to concede another goal very similar to that against Man Utd, which led to a tight finish to the game, but thankfully this time we held out. Job done.

In Robbie We Trust

Today was mostly taken up by tutorials, and a very enjoyable dinner party courtesy of my friend Maria. The real shock news of the day, however, was the return of Robbie Fowler to Liverpool - every story on the front page Liverpool website is about this, and about 30 pages of the BBC 606 messageboard too.

I'm a bit worried to be honest. He clearly passed his best - indeed, probably about 5 years ago (when we first sold him) - and bar a couple of recent goals has hardly shone for Man City. Still, he'll always hold a place in the heart of Liverpool supporters, because he'll always be a red, and his 171 goals (so far) for us include the fastest ever Premiership hat-trick.

Whether the re-union will turn out to be a good move or not only time will tell. I don't know if Robbie will figure that prominently, but he is a more natural goal-scorer than any of our other strikers (possibly bar Mellor - shipped on loan to Wigan earlier this week), so he might even teach them something on the training ground. Still there aren't many legendary strikers available on a free transfer and not cup-tied in Europe. Whatever my doubts, I've had a big grin on my face since I heard the news, and I defy any other red not to be pleased.

Our Fowler, thou art is scoring,
Robbie be thy name, Thy time has come,
Thy transfer has been done,
On a free as it is January,
Give us this day our favourite red,
Alonso will give you the best passes,
As Carra stops those who pass against us,
Deliver us the title and not in to relegation, for nine is your number,
Cisse can have fourty, forever and ever, our man.

Presentations and Karl

Today I made my second presentation in the snappily-titled Oxford University Political Theory Graduate Students' Research Workshop. I won't post the whole paper here, because it's too long, but you can see the ideas here.

Also I went to see my friend Karl play another gig at the Phoenix picture house. Although he only played a short set, and without Cisse's vocals, he did play a cover of Ugly Kid Joe's '(I Hate) Everything About You' which I hadn't heard before, and one of his friends did a fine Radiohead impression.