Happy Birthday me

NYE is a pretty crap time to have a birthday. Everyone's busy - often out of town - and even those that aren't don't really want to go to your birthday. One friend complained about having to go to birthday parties rather than having a 'real NYE'. I wouldn't know, I guess I'll never have a normal NYE because it will always be my birthday... Perhaps consequently, I don't really see the fuss about NYE and would've thought a friend's birthday more important...

[UPDATE: What I did] Anyway, I went into town and spent money on books, CDs and DVDs (i.e. the usual) then had a few friends over for wine, conversation and Auld Lang Syne in the evening. Thanks to those who made it.

Liverpool 1-0 West Brom

I feared this was going to be one of those games where the ball just won't go into the net. Some great saves by the WBA 'keeper (I can see why he's keeping Kirkland out the team) but well done Crouch for knocking up another goal - hope he can continue for the second half of the season, as he did last year. 9 points out of 9 over Christmas now.

Oxford

Back in Oxford today. Despite snow, ice and weather reports, the journey was uneventful. Hardly worth getting up at 7am for!

Everton 1-3 Liverpool

Too bad we lost our clean sheet record, but any derby win is a good one. Cisse took his goal particularly well, which was pleasing to see.

Liverpool 2-0 Newcastle

I was in a pub with friends for this one (including a Newcastle supporter), but sadly not one showing the game. Michael Owen’s return to Anfield was a let down, for him at least. The problem with Newcastle is that, despite being an attacking team, they don’t seem to get much service to their strikers.

The sending off of Bowyer finished the game as a contest really. On another day, Crouch and even Gerrard could have been in trouble for the ensuing fracas, but I’m glad they weren’t. Besides, it could’ve finished 7-a-side then…

Home

Afraid I came home Friday night, only to find we've been having internet problems. Updates are likely to be sparse until I'm back in Oxford. Have a good Christmas everyone.

Sao Paulo 1-0 Liverpool

So, a record-breaking run of eleven clean sheets ended as Liverpool lost the worlc club championship final. Quite how, I'm still not sure. The statistics I saw said we had over 60% of possession, over twenty shots (to their five) and seventeen corners (to nil). That's to say nothing of three disallowed goals...

Anyway, I'll stop complaining before I sound like Gerard Houllier. The fact is the best team doesn't always win, and while it's frustrating to lose a final like that, I'm proud of our players.

I have to say I was slightly baffled it took so long to make changes. Although we were creating chances, we weren't taking them. Personally I'd have thrown Crouch and Cisse on around the hour mark. (Though this is only 'what I'd have done' - and I'd never claim to be a better manager than Rafa...)

I was happy to see FSP involved again. He's never looked too much of a goal-threat for us, but he's quick and skillful, and could develop into a Garcia-style tricky customer. I'd like him to get more first team chances.

Conference

Despite my cold, I'm attending the British Academy Conference on Democracy, Equality and Justice this weekend. Since London is half-way back home to Colchester, I'll be using the opportunity to return home for Christmas too.

Liverpool 3-0 Deportivo Saprissa

Although I'd had a dream that Liverpool lost (2-1 I think) this match should never have been much of a challenge, and it wasn't. Despite Josemi and Traore playing, we maintained our run of clean sheets - 11 a new club record. Josemi actually quite impressed me at times to, but then the opposition we weak...

Crouch scored two more goals - and since he was also credited with the dubious Wigan one, I suppose that's technically a hat-trick today! Cisse linked up well. Perhaps he was trying to show what a team player he was, but I don't remember him taking a shot... Also nice to see Pongolle on (and it didn't surprise me it was for Gerrard). He made a good run as soon as he came on, and after a clever flick from Cisse was unlucky not to score (or win a penalty)

Roll on the final...

Selective Attention

Last night I suddenly came down with a nasty 'flu type cold. The kind where my nose and head are all bunged up, joints ache, I'm tired and bright light is a bit painful. No, not a hangover...

Anyway, I've spent most of today lying around on my bed under a blanket and feeling sorry for myself. A shame, because I not only had to cancel plans to go to goth night at the Cellar with Nick and Christian, but I'm supposed to be going to a conference Friday. Don't know if I'll feel up to that now. That aside though, it's been a nice day...

"If you take the scrum out of the equation, we played well."

Former Australia coach Eddie Jones, defending the Wallabies' defeat by England.

"If you take the assassination out of the equation, the President and Mrs Kennedy quite enjoyed the drive from Dallas to the airport."

Mike Carlton (Australian broadcaster) disagrees.

Source: beeb.

Classic Movies

Last night we (me, Karl, Ayelet, Kieran and Miriam) were discussing favourite and classic movies, having just watched Monster. I found this amusing quiz on Rob's blog:

What Classic Movie Are You?
personality tests by similarminds.com

Man USA out of Europe!

I normally like to support British teams in Europe. If Liverpool don't win the CL again, I wouldn't be upset if Arsenal do. Unfortunately the other three English teams (Everton, Man Utd and Chelsea) are all hated rivals, which makes it harder to support them - and even funnier that the second have now tumbled out.

Is this the real life
Is it just fantasy
Crashed out of Europe
Can't escape mediocrity

Open your eyes look down on the pitch and see
We're just a poor side
Undeserving of sympathy

Because he's chewing gum, a little slow
Little skill, little show
Any way the score goes, doesn't really matter to us, to us

Gaffa just missed the goal
Put the ball against my foot
Kicked it over by 10 foot

Gaffa the match had just begun
But now we've gone and thrown it all away
Gaffa oooooh didn't mean to make you cry
If you're not here again this time tommorow
We'll carry on carry on, cause money's all that matters

Too late our time has come
We have got yellow spines
And we're losing all the time
Goodbye everybody we've got to go
Got to leave and catch the plane because we're out
Gaffa oooohh our end it seems is nigh
It sometimes seems we didn't deserve it at all

I see a little silhouetto of a man,
Glazier Glazier
Has he skinned us for our money
Stevie G and Carra very very frightning me

Dirty Keano Dirty Keano
Dirty Keano had to go
Tragicooooooooooo

I'm just a poor boy nobody loves me
He's just a poor boy from a poor family
Spare him his life from his monstrosity

Rio's poor, looks a sight, time to let him go
Van Nistlerooy he looks just like a horse (Like a horse)
Van Nistlerooy
He looks just like horse (like a horse), looks just like a horse (like a horse) looks just like a horse
Like a hooooooorse, horse, horse, horse, horse, horse, horse, horse
Oh Glazier, Glazier thank you for buying them

Beelzebub, have the devils got a side today
So you think you can hoof it, for fat rooney
So you think that Ronaldo, will save you the day
Ooohhhh ManU, its so funny ManU
You've just gotta crash out, just gotta crash right out of here
Nothing really matters, its just about cash nothing really matters its all about the money

Anyway the score goes...

(From BBC 606 messageboard)

BA (Hons) Spam

Today I received the below email:

Subject: Admissions Office - emailing
From: "Patrice Durham - MBA, PhD"
Date: Sun, November 27, 2005 5:09 pm
You've been nominated,
Thanks to a private nomination, you are now eligable to obtain an official University Degree.
Obtain a prosperous future, increase money-earning power, and the [sic] enjoy the prestige that comes with having the career position you've always dreamed of. The degree will be awarded to you based on your present knowledge and life experience, bachelors, masters, phd and more are available.
If you are serious about this, please call us back ASAP at 1-206-338-3579
Sincerely,
Patrice Durham - MBA, PhD - MBA, PhD
-Admissions Officer

I already have BA (1st class) and, though not yet graduated, an MPhil in Politics. I'm working toward my PhD. Somehow, buying a dodgy degree online doesn't seem so appealing... Nice of them to try though!

More mild amusement, this list of ill-chosen URLs.

7th Week Round-up

Round up: Thank goodness it’s now the start of 8th week. I’m looking forward to the end of term… Last week was crazily busy. Tuesday I ended up getting a late spot on the New College exchange dinner, and met a guy (Paul) from my department just starting a PhD there. I’d seen him in seminars, but having dinner together gave us a chance to get to know each other properly.

Thursday, after our Political Theory Workshop, we traditionally go to the Kings Arms for drinks. This week I’d been planning on getting food too, since I was going on to the Jurisprudence Discussion Group, but Paul suggested New College bar, since it was cheaper and closer than KA. So I ended up back there, and had to go to the law seminar on wine but no real food… It was a good talk though, about deliberative democracy, and I got to say rather a lot (since those lawyers don’t work so much on democracy). Prof John Gardner was there, and joined us in the KA afterwards – where on leaving I met Paul and some of the other Politics students, also leaving the KA where they’d gone after New!

Prof Gardner not only bought me a drink, but invited me to his annual Jurisprudence party Friday, so that gave me another night out, and again without dinner… And Saturday was the CSSJ conference, so again no dinner, and New College bar afterwards, for the third time in a week!

Man City 0-1 Liverpool

I didn’t see any of this match, owing to being at the launch of the Oxford Centre for the Study of Social Justice conference.

From the sounds of it, Liverpool were hardly fluid, but ground out a 1-0 win, which is exactly what we need to be doing to maintain our progress up the table.

The main talking point seemed to be the minute’s silence for George Best cut down to about 20 seconds. It was hardly surprising that a Man City/Liverpool crowd wouldn’t be keen to respect someone so connected with Man Ure. I know a number of people were unhappy with the decision for a national minute’s silence, given he wasn’t even English, and had pissed his life away.

It’s interesting to note he was applauded at Wolves, Celtic and (I think) Old Trafford. This, I’m told, is the continental approach, and far more sensible. It allows any who don’t agree to ‘voice’ that by not clapping, yet without spoiling the overall effect – as with those who talked in the silence.

Rehfeld on Random Constituencies

B). Rehfeld

At this stage, we could consider even more radical proposals. Andrew Rehfeld[1], for example, proposes abandoning territorial representation altogether. He argues that large constituencies don’t in any case represent communities anyway. Rather the consequence of territorial representation is that legislators are more concerned with pushing local pork (like our ‘divide the 10 Euros game, last week) than promoting the common good. As an alternative, he proposes random constituencies: On coming of age, every American will be assigned to one of 435 constituencies, which will be theirs for life. As a consequence, each representative will truly represent a cross-section of the nation, providing “self-regarding incentives to act as if they cared about the common good” [p.xiv].

This radical suggestion challenges many of our ordinary assumptions. Rehfeld seems right to point out that territorial representation – even if deeply embedded in the US by the federal system – isn’t necessary; the slogan ‘all politics is local’ is true in consequence of the system, and we could go for representation by occupation or ethnicity. Rehfeld goes even further in disputing the presuppositions of our current topic, when he suggests district equality doesn’t matter:

“Despite its democratic-sounding framing, this “equal chance” claim in fact reflects one of the least democratic values we could imagine, as if everyone should have an equal chance of individually deciding an election, each of us standing an equal chance of being our own petty tyrant for a day… [W]e properly should not worry about unequal distributions of inconsequential goods, and an individual vote in a large election is as inconsequential good as any” [p.11].

This poses an interesting challenge, and radical alternative, to our present concern. My disagreements with Rehfeld will require more thought (and for me to finish reading his book first) – though it goes without saying that, while I’m happy with the use of randomisation, I’ll have to dispute the above claim. For now, some provisional remarks:

If votes aren’t equal, we aren’t giving all people equal concern and respect. If votes are ‘inconsequential’, it isn’t clear they’re any good. But votes aren’t just of symbolic value. Suffragettes surely wouldn’t have been happy if women were granted ‘half-votes’.

Moreover, equalising the value of votes seems the safest way to make sure they all count at all. One problem with weighted-voting is that one’s share of power need not be proportional to ones number of votes – a fact Rehfeld seems either ignorant of or to forget [p.42][2]. If votes are split 3, 3, 3, and 1 (with 6 needed for a motion to pass) the fourth person has no voting power – they are never vital to any passing motion, as it always requires at least two of the others, who are sufficient themselves[3]. If we allow even what seems a small inequality, it may have a great effect, to the extreme of denying some any influence whatsoever. If we want votes to have more than symbolic effect, the best thing to do is make them equal.

Finally, I think Rehfeld’s proposal would give majorities too much power. Territorial districting works because the population isn’t evenly distributed. If the population was clustered, one could achieve approximately proportional results, but districting accordingly. Alternatively, however, if the minority are split over many districts, and lose them all, they have no representation at all. Rehfeld suggests that some minorities may be better served by having a voice in all districts, rather than controlling a few but being anonymous in most [p.11]. This is an empirical question, but I’m still unhappy with the consequence he envisages and accepts – that a 51% majority could win 100% of the seats [p.244].

In any case, while Rehfeld seems happy to accept majority-rule in his random constituencies, and declares himself not bothered by any inequality of votes, his proposal does not directly contradict my lottery-voting. He is at pains to stress that defining districts is something independent from, and prior to, determining voting procedures [e.g. pp.7, 21]. Once a district is randomly constituted, it is still an open question whether to adopt majority rule[4].

In commenting on PR and group rights, Rehfeld says:

“If constituencies are defined by their members’ similarity of voice (if African American representatives, for example, come from predominantly African American districts), then we promote diversity of voice within a representative body by denying it within the constituency. The demand that representative bodies should be diverse thus subordinates the deliberative diversity within a constituency to that of the legislature. Yet, if good and proper deliberation requires that all voices are heard, then it would appear that we have to choose between diversity within the legislature and diversity among their electoral constituents. Or, in terms of exclusion, the question becomes, do we exclude “voice” from the representative body itself, or from the constituent groups who select their representatives?” [p.27]

He may be right that a diverse legislature is often ensured by creating homogeneous electoral groups, and further that such groups (exposed only to their own viewpoints, not others) may radicalise, making legislative compromise harder. However, the suggestion we must choose between a diverse legislature and diverse constituencies is a false dichotomy – and even if it were not, Rehfeld is not necessarily right to opt for the latter, given the former is where real decision making (if not local participation) takes place. It’s quite possible to adopt randomly-assigned constituencies (a la Rehfeld) and lottery-voting, and thereby produce diverse constituencies that mirror the whole nation, and a legislature that also includes members of all these groups. (Since both procedures rely on randomisation, neither are logically guaranteed – but the numbers concerned make these generalisations pretty much absolute).

In any case, Rehfeld’s preference for diverse constituencies seems to presuppose that democratic deliberation has to take place with fellow constituents [p.51]. Non-territorial constituencies, he supposes, only became possible with mass media and particularly the internet – through which he imagines most debate and campaigning taking place [pp.243-4, c.f. p.60]. I haven’t yet found any reason why deliberation has to be with fellow constituents, rather than simply with any others (preferably perhaps of somewhat opposing views). While it’s true that the internet has allowed for much democratic debate, e.g. political blogs[5], it seems unlikely to me that citizens would deliberately seek out others with whom they had no more than a randomly-assigned constituency in common – it’s far more likely they will converse with those local to them and/or sharing similar interest/views.

I think Rehfeld and I disagree about as much as we agree on[6], but his work is useful because it highlights that the very question we are here answering – how to assign representatives between states – may itself be flawed. However, I suggested arguments above against his indifference to the (in)equality of votes. If we are concerned about equality, then even if we were to adopt non-territorially based constituencies (on whatever lines you might imagine, e.g. profession, ethnicity or randomisation), then we would still need a method of apportionment between these groups. I don’t believe Rehfeld’s under-developed criticism of equality is successful, so I do not think he casts doubt on the importance of our present inquiry – only raises an important question about whether we should be apportioning to territory, as opposed to something else.

C). Conclusion

Use of territorial constituencies is just one historical prejudice too often accepted as a given, however. A further value in Rehfeld’s work is bringing random methods to more prominence, even though I don’t agree with exactly where he uses them. This takes me back to the lottery method so quickly dismissed by Balinski and Young (p.66, p.74). They say “A basic problem with a betting man’s method is that, although it may be “fair” over the long run, the immediate outcome is almost sure to be unfair” (p.67). However the only reason they say it is ‘almost certain’ to be unfair is their less plausible assumption all seats (rather than just remaining fractions) should be assigned randomly. The latter method, because it sticks within the quotas (rounded up/down) can be said to be fair in both the short term and long term. While the lottery may seem to go in favour of a state with a weaker claim on one occasion, there is no systematic bias involved.

To dismiss such (partly) random methods out of hand seems, to me, far too quick. Of course, to return to their quotation (p.93) with which I opened, electoral systems as a whole are confined by feasibility – in part, what people will accept. If the US public are hostile to the perceived ‘irrationality’ of random methods, then it is unlikely they will be the best to adopt. While it’s true there is a tendency to choice in modern society[7], there is also a counter-current against ‘hyper-rationality’, with many advocating random methods when ‘reason(s) run out[8]. It’s far from clear what public opinion is when it comes to lotteries. Whatever the rationality of such procedures, it’s almost universally accepted that they’re fair. If we want each person to be counted equally – in the sense of having an equal chance to make a difference – there seems to be no objection to bringing more chance into the procedure.
[1] See note 2.
[2] This gives me a feeling of smug superiority, even if it doesn’t itself discredit his whole argument!
[3] Such examples can be found in J. F. Banzhaf III (1965) ‘Weighted Voting Doesn’t Work: A Mathematical Analysis’ Rutgers Law Review 19 317-343 and A. D. Taylor (1995) Mathematics and Politics: Strategy, Voting, Power, and Proof ch.4, where he shows Luxembourg had no power in the 1958 EEC split of 4, 4, 4, 2, 2, 1.
[4] Rehfeld (2005) p.7 “Maybe they would use majority rule or plurality rule. Maybe they would select a representative by lottery. Our concern here is not, then, with voting rules or the questions of single-member or multimember representation. It concerns the prior question of how constituent groupings themselves affect the legitimacy of a political regime.”
[5] E.g. a few quick links take me to (amongst others): http://considerphlebas.blogspot.com/, http://users.ox.ac.uk/~magd1368/weblog/blogger.html, http://politicalarguments.blogspot.com/, http://crookedtimber.org/, http://bensaunders.blogspot.com/, http://noconceptofliberty.blogspot.com/, http://left2right.typepad.com/, http://www.makemyvotecount.org.uk/blog/, http://opendemocracy.typepad.com/wsf/…
[6] Nonetheless what two people share can be as illuminating as what they disagree on. It was recently put to me that G. A. Cohen shares, with many pragmatists and continental philosophers (e.g. Rorty and – I think – Habermas) a belief that if there’s no objective truth, normative political philosophy is in need of major revision. This agreement is itself significant, though they disagree about the conditional (i.e. Cohen thinks there is a truth…).
[7] See, e.g., A. Buchanan, D. Brock, N. Daniels and D. Wikler (2002) work on designer babies, From Chance to Choice: Genetics and Justice.
[8] See, e.g. N. Duxberry (2002) Random Justice: On Lotteries and Legal Deciison-making; J. Elster (1979) Ulysses and the Sirens: Studies in rationality and irrationality and (1989) Solomonic Judgements: Studies in the limits of rationality; D. Heyd ‘When Practical Reasons Plays Dice’ in E. Ullmann-Margalit (ed.) (2000) Reasoning Practically; and O. Neurath (1913) ‘The Lost wanderers of Descartes and the Auxiliary Motive (On the Psychology of Decision)’ in his (1983) Philosophical Papers 1913-46 [ed. and trans. R. S. Cohen and M. Neurath].

US Apportionment

Theory of Voting paper in two parts again this week, because it's a long one - but also my penultimate (you'll be glad to hear)

What System of Apportionment of US Congressional Districts to States is the Best?

Balinski and Young point out “The ultimate choice in any nation must, of course, depend upon its political, social, and legal heritage” (p.93[1]). This questions whether there is any one best system. Further, there is a difference between arguing in the abstract for one principle or method of apportionment, and arguing for what should be applied in a particular context, e.g. the US Congress – which is more constrained by cultural possibilities, and subject to particular details (e.g. representing minority groups). Nonetheless, my discussion will be rather abstract, but focus on the US.

First I outline six historical procedures, and compare their merits, following Balinski and Young. I question, however, some of these authors’ normative claims, in particular about fairness and lotteries. I go on to discuss a radical alternative, proposed by Andrew Rehfeld[2], for random constituencies. I criticise many details of his plan, not least his neglect of equality, but think there is something to be said for randomness, and I use this against Balinski and Young’s rapid dismissal of ‘roulette methods’.

A). Balinski and Young

Article 1, section 2 of the Constitution provides that “Representatives and direct Taxes shall be apportioned among the several States which may be included within this Union, according to their respective Numbers” (quoted p.5). This is, however, totally vague in that it doesn’t specify how representatives are to be apportioned according to numbers. There are infinite logical possibilities (pp.63-5), we shall see some of the important methods historically proposed, but for now note it doesn’t even logically require direct proportion between representatives and population (though this is obviously what’s normatively desirable) – some form of inverse proportion would also be ‘according to numbers’.

Six historical methods:

(1) Jefferson (p.18) – fix a divisor (e.g. one seat per 34,000 people) then find the resulting number of seats for each state. E.g. a state with 76,000 people would have two. All fractions are rounded down.

(2) Hamilton (p.17) – fix the number of seats and then find a quotient (US population divided by number of seats). Give each state the whole number part of their quotient. Distribute remaining seats to those with the largest fractions (so if one state should have 1.88 seats and another 6.27, the actual distribution is 2 and 6).

(3) Adams (p.27) – fix a divisor and give each state their quotient, with fractions rounded up – thus 1.02 becomes two and 5.98 six.

(4) Webster (p.32) – find the divisor so whole numbers nearest quotients add up to the required total.

(5) Dean (p.29) – make the quotient as near to the divisor as possible, e.g. in 1830 Massachusetts had a population of 610,408 which divided by 13 was 46,954 and divided by 12 was 50,867 – thus they got 13, as this was closer to the ‘target’ of 47,700.

(6) Hill(-Huntington) (p.47) – make the representatives to seats ratio as near to uniform as possible, with divergences measured in relative percentage terms (unlike Dean’s absolute).

Balinski and Young reject Hamilton’s method in favour of the divisors because of what’s come to be known as the ‘Alabama paradox’ (pp.39-42, c.f. pp.68-9). In 1880, it was noticed that the Hamilton method would give Alabama eight out of 299 seats, but only seven out of 300. This is because Alabama’s quotient of 299 was 7.646, which was rounded up to eight (being one of the largest remainders). An extra seat increased this by 0.33% but because this was a larger absolute increase for larger states, Illinois and Texas ‘leapfrogged’ Alabama in the queue for extra seats – they now had fractions rounded up, while Alabama’s was rounded down. This isn’t an isolated incident – in 1900 it was particularly worrying to find that Colorando would get two seats out of 357, but three out of either 356 or 358, and that as the total changed from 350 to 400 Maine’s delegation moved back and forth between three and four (pp.40-41).

One consequence of this is that state A can grow in size relative to state B, and yet still lose a seat to B. in 1900, for example, Virginia’s share of 386 seats was 9.599 (rounded up to ten), while Maine’s share had been 3.595 (rounded down to three). Virginia’s population was growing by 1.07%pa and Maine’s by 0.67%pa, both less than the national average (2.02%pa). Thus by 1901 their shares were 9.509 and 3.548 – Virginia had declined more in absolute terms because it was larger, and so lost a seat! Another perversity is that the addition of Oklahoma in 1907, which had five extra seats, added to the legislature, resulted in New York transferring a seat to Maine (p.43).

I think Balinski and Young may be too troubled by these paradoxes. They claim:

“Intrinsic to the idea of fair division is that it stand up under comparisons. If an estate is divided up fairly among heirs, then there should be no reason for them to want to trade afterward[3]… [Further] any part of a fair division should be fair” (p.44)

If we take fairness to mean equality, then it is obviously a relational ideal. One can’t be equal without being equal compared to someone. There are, however, other possible meanings. If fairness was a matter of satisfying desert then, assuming we can measure desert without comparison, we can also judge fairness. If I deserve ten, and have ten, then my absolute claim is satisfied[4]. Whatever we think of the first claim, the second – that parts of a fair whole must be fair – seems even more controversial. Suppose we divide £30 between three people, £10 each. Is it fair that the first person in isolation gets £10? It seems we can only call the part fair in virtue of the whole. Perhaps that’s just sophistic, but consider a further case of compensating inequalities. Suppose we are dividing food between two people – we have one bit of meat and three potatoes. A fair division may well be to give one person the meat and one potato, the other two potatoes[5]. Can we say that the division of potatoes part (1,2) is fair though?

In any case, Balinski and Young go on to conclude “No apportionment method is reasonable that gives some state fewer seats when there are more seats to go around” (p.42). Presumably, this is meant with a ceteris paribus condition implied – for it seems fine to give one state fewer seats if it has shrunk in absolute or relative population. The reason the Alabama paradox is problematic is that representation varies (up and down) simply with the total size of the House, nothing else changing. It is true that these paradoxes are worrying, but it’s also true that deviation from quotients is worrying. Although it requires divisor methods to avoid the population paradoxes they don’t (unlike the Hamilton method) guarantee that state’s representation is within +/-1 of their initial quotient (i.e. rounded up or down) (p.79).

Balinski and Young advocate the Webster method, because it avoids the population paradoxes, is unlikely to deviate from quotas (one time in 1,600 (p.81)), and (when it does so) shows no bias in favour of either large or small states. Their table 9.2 (p.77) illustrates expected biases:

Adams: Chance of favouring small 100%: Expected bias to small 28.2%
Dean: Chance of favouring small 93.9%: Expected bias to small 7.0%
Hill: Chance of favouring small 78.5%: Expected bias to small 3.5%
Webster: Chance of favouring small 50%: Expected bias to small 0.0%
Jefferson: Chance of favouring small 0%: Expected bias to small -20.8%

The Webster method, they argue, is intuitive because it treats fractions in a natural manner – rounding up those over 0.5 and down those under. Further this is unbiased, as every state is as likely to have a remaining fraction of over 0.5 as under. Being more generous with rounding up favours small states, being less favours large ones (p.76).

There is, however, another option that they admit is unbiased (p.74) yet reject, and that is an option involving some form of lottery[6]. As they spell this out:

“[C]onstruct a roulette wheel divided into fifty slots, one for each state, the size of each slot being exactly proportional to the population of the state. Spin the wheel and drop a small ball onto it: the state at which it comes to rest “wins” and is awarded one seat. Do this 435 times consecutively and the house is apportioned. The method is perfectly unbiased: every state is treated fairly; no one can complain that the method discriminates against it” (p.66)

This is not necessarily to describe the method in its most plausible form – indeed, they deride it as a gambler’s strategy. They immediately, however, acknowledge that one could distribute whole numbers from the quotients directly, and only randomise the fractions (p.66)[7]. On this interpretation, no state will depart from its quote (rounded up/down), and there is no bias; though population paradoxes remain, they will be partly the consequence of chance (and as such, it’s not so clear they’re problematic).

[1] All references in parentheses refer to M. L. Balinski and H. P. Young (1982) Fair Representation: Meeting the Ideal of One Man, One Vote.
[2] A. Rehfeld (2005) The Concept of Constituency: Political Representation, Democratic Legitimacy, and Institutional Design. All references in square brackets refer to this book.
[3] C.f. Dworkin’s envy-test: “No division of resources is an equal division if, once the division is complete, any immigrant would prefer someone else’s bundle of resources to his own bundle” (2000) Sovereign Virtue p.67.
[4] This claim is complicated if we distinguish absolute and relative desert. (I shall illustrate this with a case of non-desert claims, for simplicity). Imagine A owes B £10 and C £20, but A only has £15. He could give B £10, which would fully satisfy B’s claim. This, we might say, would be unfair to C, however, who will only be 25% satisfied. Other things equal, it would be better to give B £5 and C £10, satisfying each 50% of their claim. I put this aside too.
[5] Assume this is fair, by hypothesis. The envy test would make it depend on parties’ preferences between meat and potatoes. If both very much want the meat, it might be better to make the ‘choice’ between meat or all three potatoes. I think it’s worrying that if one person’s vegetarian, the fact he doesn’t want the meat effectively makes it cheaper for the other – implying (meat + 1.5 potatoes) for the omnivore and (1.5 potatoes) for the vegetarian are equal as neither envies what the other has…
[6] In fact, this is just one option preserving proportionality elsewhere in the system – here in chances. There might be other alternatives sites of proportionality, e.g. one could weight representatives’ votes to reflect populations. I leave that problem to next week…
[7] Rawls mentions something similar in A Theory of Justice (1971 p.223/1999 p.196) “the precept of one elector one vote implies, when strictly adhered to, that each vote has approximately the same weight in determining the outcome of elections. And this in turn requires, assuming single member territorial constituencies, that members of the legislature (with one vote each) represent the same number of electors… [S]afeguards are needed to prevent gerrymandering, since the weight of the vote can be as much affected by feats of gerrymander as by districts of disproportionate size… [In the ideal world] Political parties cannot adjust boundaries to their advantage in the light of voting statistics; districts are defined by means of criteria already agreed to in the absence of this sort of information. Of course, it may be necessary to introduce certain random elements, since the criteria for designing constituencies are no doubt to some extent arbitrary. There may be no other fair way to deal with these contingencies.” Note how readily he accepts random methods!

Liverpool 0-0 Real Betis

We need at least a draw tonight. Hopefully we should get it, and wrap up qualification for the last 16 of the CL. I'm going round my friend Rob's to watch it.

In the meantime, this Liverpool squad selector made me laugh.

(My, more realistic, team for tonight: here)

UPDATE: The result was a fairly boring 0-0 draw but it was enough to ensure qualification. A shame Crouch still didn't break his duck - though he was stopped only by a handball from taking one of several good chances we created.

Thesis Pointers

I keep getting the nagging feeling my PhD will carry on for ever, as I haven't really written anything since finishing my Masters in April. At the moment, the intention is to start remedying this over the Christmas 'vac' - though I don't work too well in the cold (it's taken me all day to cobble together 2,000 words about what I was recently reading for next week's Theory of Voting class paper - to be posted here of course), and I'm sure plenty of other distractions will come up (academic and less so).

Anyway, for those similarly struggling, Crooked Timber has what looks like some very good advice here.

Liverpool 3-0 Portsmouth

I only followed the game online, while working, and am going to a birthday party tonight so won’t get to see MotD. Still, sounds like another good result for Liverpool, with Cisse and Morientes both scoring.

Too bad Crouch’s duck continues – with a saved penalty and all – but by most accounts he played pretty well. I don’t think it counts as an assist (to the much improved Zenden, who got the rebound) though.

My main concerns are injuries to Garcia and Alonso. No word from LFC on how bad those are as of yet, but hopefully they’ll be fit for next weekend. I think since we can probably afford to rest them (on the bench) for the Betis clash we should.

From the BBC 606 Messageboard: "Alonso was clearly stuggling and limping off the pitch and Finnan passes the ball to him when he can hardly walk! Fair play to Alonso, got the ball, back heeled it to one of our players then hobbled off."

Commiserations to my flatmate Glyn, who saw Southampton turn a 3-0 lead into a 3-4 defeat in the last 20 minutes this afternoon.