Tuesday, May 30, 2006

Blogger Meet

A date, time and place have been confirmed (and repeated here) - tomorrow, The Bear (near Oriel/beside Christ Church), 8pm.

Also, while I'm here, happy birthday Rachele.

Sunday, May 28, 2006


I'll have to come back to IIA, which has always seemed (to me) the most confusing of Arrow's conditions. So here's the third in my series of posts, on non-dictatorship:

(5.8) Non-Dictatorship

5.8.a Plausibility

Arrow’s Condition 5 is that the social welfare function is not to be dictatorial. He elaborates this by adding “A social welfare function is said to be dictatorial if there exists and individual i such that, for all x and y, x Pi y implies x P y regardless of the orderings R1, … , Rn of all individuals other than i, where P is the social preference relation corresponding to R1, … , Rn”[1].

As long as we are dealing with democracy, this seems uncontroversial – indeed, it seems definitional that democracy (rule of the people) involves many, as opposed to monarchy. Once one person always determines the ‘social’ ordering – like an absolute monarch – we seem to have left behind the area we’re interested in[2]. There might be reasons why a dictatorship may be advantageous, at least in certain circumstances (e.g. emergency powers), but it is clear that we have left behind the arena of collective choice – or, more precisely, we would be dealing only with one individual making choices for a collective, rather than decisions by a collective. Yet if one individual was to determine the final outcome, there would be no point in asking all the others[3].

The key point to note is that an Arrovian dictator decides for all x and y, that is her preferences determine all issues. One may perhaps want to say that if i can solely determine the choice over a single issue (say, kPil implies kPl even if for all other individuals lPjk) then i is a dictator over that issue, but Arrow does not use the term that way. MacKay introduces the term ‘vicious’ to describe such rules, that allow one person’s preferences to prevail, even over the opposition of all others[4]. But despite this morally-loaded term, it is not clear ‘vicious’ rules are necessarily a bad thing. Indeed, those who accept some form of liberal private sphere or self-regarding rights[5] generally accept that each should be decisive over some set of decisions. In any case, this is not a dictatorship in the technical sense used here. A rule is only dictatorial if one specified individual decides all issues. This is actually very weak – it technically leaves open the possibility that i decides for all x and y, except for k and l.

Two further details remain: Firstly, what if everyone wants a dictator, and secondly how is the conditional implication to be understood? On the first, Arrow says, “the desires of those individuals [can be said to] include a liking for having social decisions made by a dictator or at least a liking for the particular social decisions which they expect the dictator to make”[6]. In Chapter VII, he goes on to briefly consider the possibility of higher order preferences for a decision-mechanism conceived of as a value itself – for example, whatever our preferences between x and y, we might prefer x-arrived-at-democratically to y-arrived-at-in-other-ways. In such circumstances, we cannot rule out that “the desire for a dictatorship or for a particular dictator may be overwhelming”, in which case “our social welfare problem may be regarded as solved since the unanimous agreement on the decision process may resolve the conflicts as to the decisions themselves”[7]. It is, of course, quite possible that all would prefer to defer to an authority they accept, e.g. the pope[8], and this can be understood either as them having a higher order preference for what he decrees, or as them revising their lower order preferences between x and y in light of what he says (‘I must have been wrong, x is better for me after all’). I think Arrow is right to regard such as an acceptable solution to the social choice problem, however. While they may formally appear to be dictatorships – because the pope’s preference over x and y determines the social ordering – this is so only because others (unanimously) accept the authority. As such, it seems a consequence of Pareto that the social choice must conform to these preferences[9].

This brings us to the related point, how one should understand Arrow’s “if there exists and individual i such that, for all x and y, x Pi y implies x P y”[10]. One natural understanding is as a material conditional: it is true iff in all circumstances where xPiy then xPy. This, however, seems to miss something from an ordinary, intuitive understanding of implication – one that, at least implicitly, involves the idea of causation. We think i is a dictator if it is because xPiy that xPy. Conversely, we do not necessarily think there is anything untoward simply because whenever xPiy it is also the case that xPy. Consider the example of an individual with higher order democratic preferences. It may be that she is able to transform her preferences, perfectly and instantaneously, so that whenever xPy (as the democratic outcome of social choice), her preferences are xPiy. In this case, it will also be true that whenever xPiy so also xPy, but this does not seem to be a case of dictatorship. I think the implication Arrow is talking about has to be a stronger sense. It has to be that in any possible world[11] where xPiy then it follows that xPy, which comes pretty close to saying xPy because xPiy[12]. Understanding dictatorship as requiring something stronger, of course, makes the requirement of non-dictatorship on our choice procedure weaker. I think it is clear, however, that – subject to the considerations of the previous paragraph – a social choice procedure must be non-dictatorial, or it is simply not a social (collective) choice at all.

5.8.b Lottery-Voting Assessed

In lottery-voting, a single person is picked to decide a given issue. Since this effectively disregards all other preferences, the rule is what MacKay would call vicious. Despite the fact it is often informally called a ‘random dictator’ method[13], it is not, however, dictatorial in Arrow’s sense. There is no individual whose preferences automatically determine all social choices. While i might be drawn to decide this issue, next time it might be j. The randomness means that, even in the sense in which each is a quasi-dictator, each has an equal chance to be so on each occasion.

Random selection is not, however, taking turns. While over a large number of persons and issues, it is likely power will change hands regularly – even if not everyone gets a turn – we might worry that one individual might receive more than her fair share of power as a result of mere fluke. For instance, suppose we have ten individuals (a-j) and ten issues to resolve. It might be convenient if each individual got to decide one of the issues[14]. If we leave who decides to random chance, however, then it is logically possible that an individual – say, d – may get to decide all ten issues[15]. Does this mean that because, on each issue, xPdy determines the social choice, d is a dictator? No, this is merely a case where d’s preferences happen to coincide with the social choice, but that does not make d a dictator – for d’s preferences would also coincide with all the social choices if there was unanimity over each issue. For d to be a dictator, her preferences have to prevail in all possible worlds. Even if it happens that d’s preferences do determine each and every social choice, it is not the case that they always do so simply because they are d’s. It could have been that someone else’s vote had been drawn on any of the issues. Thus even in this vanishingly rare possibility, lottery-voting does not violate non-dictatorship; for while only one person’s vote ultimately counts, it gives each an equal chance of being the decisive one over any given issue.

[1] Arrow (1963) p.30
[2] T. Pratchett (1987) Mort “Ankh-Morpork had dallied with many forms of government and had ended up with that form of democracy known as One Man, One Vote. The Patrician was the Man; he had the Vote” p.176, fn.
[3] MacKay (1980)
[4] MacKay (1980) p.105.
[5] c.f. Sen ‘Paretian liberal’
[6] Arrow (1963) p.30.
[7] Both Arrow (1963) p.90.
[8] This example comes from Barry (). ‘Authority’ can be understood in terms of Raz (?); but note deference occurs to those people think are authorities, it does not necessarily follow that the chosen dictator is better at decision-making, merely accepted as so.
[9] Arrow (1963) p.74 endorses that “the condition of nondictatorship loses its intrinsic desirability” in certain conditions, e.g. complete unanimity. Thus his objection to dictatorship is not absolute. And, in any case, the ‘random dictator’ of lottery voting is not a dictator in the Arrovian sense, for he holds if an individual is decisive on a pair of issues they will be on all (pp.99-100), but this isn’t so if the decisive individual is randomly determined for each vote.
[10] Arrow (1963) p.30.
[11] I’m worried about the possible world formulation. Of course there are possible worlds where i is not a dictator. I don’t mean to claim that to be a dictator i must be necessarily a dictator. Can I appeal to something like relativised possible worlds?
[12] Note we do not need to require that not-xPiy implies not-xPy, since if not-xPiy then i must have some other preference, e.g. xIiy. (But can we assume one has prefs over all issues?)
[13] e.g. Estlund and others?
[14] Though, of course, different issues might differ in importance to different people; and some may be more concerned simply that they get their way (e.g. x) and not that they get it because it is their way (or their vote is decisive).
[15] The probability is (0.1)10.

Tuesday, May 23, 2006


Part two in my series on Arrow's conditions (following this one):

5.6.a Plausibility

Also embedded in Arrow’s citizen sovereignty is the idea that if all citizens share a preference xPiy this should be sufficient for the social choice to be xPy[1]. This is generally termed the weak Pareto condition. It actually requires something quite strong before it comes into play – namely that all citizens prefer x to y. It is because this requirement on being Pareto-satisfying is strong, however, that respecting Pareto-satisfying preferences is a weak requirement on the decision-making procedure. A decision-procedure is not required to yield xPy even in cases where all bar one vote xPiy and that one is indifferent (xIjy), only when there is unanimity.

Since the Pareto requirement merely means that unanimous preferences should be respected, it might seem so weak as to be unobjectionable. If everyone prefers x to y, and society’s preferences are to be a democratic function of individual preferences, then it would be odd for society not to prefer x to y. To use MacKay’s comparison, if one competitor is better in every respect, she must be better overall[2]. One note of caution must be sounded, however. It may be natural to assume that this will lead to better outcomes, but this is not necessarily so. Not only can preferences fail to track what is actually good but, if individuals are to vote for what is good for them, then their votes will fail to reflect ways in which the world may be better without being better for any individual[3]. The idea that outcomes can be better or worse independently on how they affect individual well-being is controversial amongst those who accept the ‘principle of personal good’[4], but there are others who argue the world can be made better though not better for any individual – for example, by being more equal or in keeping with desert[5]. Sen also argues that we should reject some Pareto improvements in order to respect individual liberty[6]. Now it seems far less obvious that Pareto is always something to be respected.

It must be remembered, however, that we are not concerned with how to achieve the best outcomes by any independent standard; we are concerned merely with a democratic decision-procedure that respects individual preferences equally. A decision-procedure, such as flipping a coin between two tied or incommensurable options, x and y, is only supposed to tell us what to do, not what is best. So it is with voting, conceived of as simply a decision-procedure. From the fact that xPiy and yPjx, we cannot infer that either x or y is ‘socially better’, but – at best – that x is better for individual i and y is better for individual j[7]. Similarly, even from the fact that xPiy and xPjy we cannot strictly infer that x is actually better than y, but what we do have is agreement. We can eliminate the Pareto-dominated option (y) because this can be done without conflict, or anyone’s objection[8]. If all prefer x to y, no one opposes the move from x to y[9].

There may be cases where we might question whether a Pareto improvement – in terms of improving an individual’s well-being – is actually an improvement in the total value of the world. Suppose, for example, we had a world consisting of Hitler and Mother Teresa, who had 4 and 5 units of utility, respectively. Now suppose we could bestow two more units of well-being on Hitler (but not Mother Teresa), moving from (4,5) to (6,5). This is a Pareto improvement, in that it makes Hitler better-off and no one worse off, but we might not think the resultant world is actually better[10]. These counter-examples are based, however, on goodness rather than preference. If we suppose Hitler and Mother Teresa (out of generosity) both prefer that Hitler receives the extra well-being, then it is unclear what democratic objection we might have. Of course, if others were added to the world, who preferred that Hitler be worse-off, then it is no longer the case that (6,5) is Pareto-preferred to (4,5)[11]. Provided we keep the focus on what is preferred, rather than what we may think is ‘objectively better’, it is hard to see on what grounds we should ignore a unanimity of preferences. While I have expressed some scepticism about when majorities should overrule minorities, if everyone prefers x to y, then this seems an easy case for collective decision-making: x is socially preferred.

5.6.b Lottery-Voting Assessed

It is easy to show that lottery-voting respects the weak Pareto condition. If all votes are for x, then necessarily any randomly selected vote will be for x. If we know everyone is in agreement, we need only ask a single random person, to give us a representative sample of the population[12]. Indeed, suggests such in his A Theory of Justice; assuming rational convergence (and hence unanimity) behind the veil of ignorance, he says, “we can view the agreement in the original position from the standpoint of one person selected at random”[13]. This is, to my knowledge, the closest he ever comes to endorsing a system like lottery-voting, and he does so only on the condition of unanimity (Pareto).

I would argue that, were we to allow for rational disagreement, and thus the possibility that individuals in the Original Position could reach different conclusions – all equally permissible by justice – it would still be fair to select and implement one such conception of justice at random. This need not be argued here, however. For now, all we need to note is that if there is universal agreement, lottery-voting will respect it, because the randomly-chosen individual must be part of a truly universal consensus. Of course, lottery-voting does not meet any stronger Pareto requirement. It may be that 999,999 individuals rank xPiy and one ranks xIjy; and yet in this case lottery-voting can (by selecting the one) report social indifference. I do not intend to discuss the plausibility of any stronger version of the Pareto requirement, however. I hope the considerations of 5.6.a have shown it is not obviously a necessary requirement on any decision-procedure. For now, I am only arguing that lottery-voting meets minimal conditions, and so it need only satisfy a form of Pareto weak enough to be uncontroversial.

[1] Arrow p.28.
[2] MacKay (1980) p.18.
[3] c.f. MacKay (1980) p.24: “however many individuals happen to prefer X to Y, that does not tend to establish that X is better than Y in any interesting sense”; Bordes () p.196.
[4] Who does? Raz? Broome?
[5] Consider, for example, a modification of Larry Temkin’s ‘sinners and saints’ example. In world one, sinners have 2 units of good and saints 10. In world two, sinners have 12 and saints 11. Everyone is better off in world two, but we might all things considered prefer world one.
G. E. Moore’s view is that anything intrinsically valuable is valuable independently of human interaction or appreciation. Thus the world would be a better one if there was breathtaking natural scenery on Pluto, even though no sentient creature would ever see it. check
[6] Sen ‘Paretian liberal’. I think he is right that no one should be forced to read a book to satisfy others’ preferences; but given there is a Pareto improvement to be had we could allow Lewd and Prude to sign an enforceable contract such that Prude will agree to read the book if Lewd agrees not to. This is no violation of individual liberty, since each agrees to give up discretion over whether he reads the book in order to satisfy a stronger preference over what the other reads, and this is done by mutually voluntary contract. We limit our own (lower-order) freedom by promises or contracts all the time, in order to achieve higher-order goals (and freedom).
[7] ‘At best’ because a preference for x does not imply that x actually is better for one. C.f. MacKay (1980) p.52.
[8] Bordes () p.196-end
[9] Note, however, that this reasoning would support a stronger Pareto requirement on the decision procedure: One that says so long as there exists an i such that xPiy, and for all others xRjy, then xPy. That is, one would only need a single individual to prefer x, so long as all others were at least indifferent – no one prefers y. Such a stronger requirement may be controversial, however: Would we really want to say a single person’s preference should decisively dictate a social preference for x if there were millions of other, all indifferent? I need not resolve this issue here; any reasoning that supports a stronger Pareto requirement will a fortiori support a weaker one.
[10] This obviously draws on Temkin’s sinners and saints example.
[11] Note that this counts these people’s external preferences, in line with the Universal Domain.
[12] Indeed, in such cases, one may think we don’t need randomness: if everyone prefers x to y, then there is no problem with a dictator – she will prefer, and therefore implement, x, and so everyone will get what they want.
[13] Rawls (1999 [1971]) p.120.


Brian Leiter confirms that the job I'm applying for is indeed Michael Rosen's, but in happy circumstances - he's moving to Harvard.

Monday, May 22, 2006


Tonight I went to see comedian Richard Herring – one half of Lee and Herring, from such TV shows as Fist of Fun and This Morning With Richard Not Judy. Admittedly, he seems to have dropped off the radar a bit since those heady heydays, but his show at the Oxford Cellar comedy night was a preview/warm-up of new material for the Edinburgh fringe. Predictably for such a small venue, the place was packed – so much so I had to perch on a barstool, and got brushed by numerous passers by, including the man himself.

I forget the name of the warm-up act, but he claimed to be Britain’s only Deaf – sorry, deaf – comedian (‘If there are any others, I haven’t heard’). He was actually pretty good, and it helped he talked about philosophy (‘If a deaf man falls over in the woods, does anyone care?’). As he said, it’s the one subject where not being able to hear lecturers – and therefore having to think for yourself – may be an advantage.

As for the man himself, I have to say that given my higher expectations I was partly disappointed. Some of his material had me in tears (see later), but some just wasn’t really funny. He had several that were either tired or quite tasteless – no doubt he’s hoping Paul McCartney doesn’t re-marry by August – and it says something he had to clarify that paedophilia, terrorism and Hitler are all bad things (‘Paedophilia numbers not going down well in Oxford’).

As I said though, there was some really funny stuff too. The best bit was probably going on about how the French call potatoes ‘apples of the ground’, and how we should respond by calling apples ‘potatoes of the sky’, just so that in French they’d be pommes de terre du ciel (pardon my French...). Also dealt very well with hecklers – but maybe it’s not a good sign that what he ad-libbed was better than a lot of the jokes he’d been working on.

Still, I don’t think I’ve ever been to a live comedy show before – at least, not a proper one, as opposed to the magician/comedian/entertainers types you get for children’s parties (‘How old are you? 6? When I was your age, I was 8’) It was an interesting, and enjoyable experience.

Saturday, May 20, 2006

Universal Domain

Excuse the unfinished footnotes, but I'm currently trying to work my way through Arrow's axiomatic requirements of social choice on a one-by-one basis. All comments very welcome.

5.5.a Plausibility

The condition often referred to as Universal Domain in the secondary literature[1] is actually part of Arrow’s Definition 5 Citizen Sovereignty: “we do not wish our social welfare function to be such as to prevent us, by its very definition, from expressing a preference for some given alternative over another”[2]. This excludes what Arrow calls an imposed ordering, where there is some pair of alternatives such that society can never express xPy even if everyone prefers x[3]. Allowing individuals and the society to express any preference ordering seems prima facie democratic. As Riker says, “Any rule or command that prohibits a person from choosing some preference order is morally unacceptable (or at least unfair) from the point of view of democracy”[4]. If we want society to be responsive to individual preferences, then it seems we cannot legitimately place restrictions on those preferences – or, at limit, if we were to restrict all preferences, society would become completely unresponsive.

There are in fact two problems with the admission of any possible preferences. Firstly, it has often been argued by liberals that there are normative justifications for excluding certain preferences, e.g. those based on religious doctrines that do not pass the standard of ‘public reason’ (Rawls), or those over how other people should behave in self-regarding matters (Mill, Dworkin, Sen). Secondly, it may result in a combination of preferences that seem likely to defeat the project of social choice.

As for the first of these problems, the idea that some preferences are, as Arrow puts it, ‘taboo’ has been a recurring one in objections to utilitarianism. Rawls, for example, contrasts the case of utilitarianism, for which “the satisfaction of any desire has some value in itself” with justice as fairness according to which “[a]n individual who finds that he enjoys seeing others in positions of lesser liberty understands that he has no claim whatever to this enjoyment”[5]. One can equally ask why a democracy should want to count the preferences of sadists, rapists and child pornographers. Nozick makes the point that individual rights restrict social choice[6], and Sen offers a case in which allowing individuals complete sovereignty over their own self-regarding private sphere defeats Pareto improvements[7]. If we think that certain issues, such as fundamental rights, warrant constitutional protection, then we thereby remove them from the domain of democratic social choice. For example, if free speech is guaranteed by the constitution, parliament cannot make a law abridging it, even if all representatives would so prefer[8].

Perhaps the reply to these worries is to insist that democracy does not always mean good government. Maybe if we want laws that ensure maximal compliance with moral demands, we are best to leave them to a group of moral experts[9]. There may be very good reasons why we would want to, for example, exclude sadistic preferences or protect free speech, but they are not democratic reasons. On this line of response, democracy is simply about responding to individual preferences, and if those individual preferences are bad, then the result is that democratic social preferences will also be infected; but the failing is with the people, not the democracy. This argument, however, runs into problems when certain preferences involve undermining the equality of others. If the sadist’s preferences are satisfied, his victim is subjugated, just as the speech of some that puts down others may ‘silence’ those groups, thereby defeating equality[10]. To take matters to a logical extreme, suppose the majority of society think the preferences of some minority should be excluded or discounted – e.g. Jews under the Nazis, or blacks under apartheid – this doesn’t make it democratic[11]. There are some cases where the logic of democracy will have to exclude certain preferences, and thus it is not clear the domain can ever be truly universal.

This brings us to the second problem, that some combinations of preferences may make a coherent social choice a priori less likely. This includes the external preferences mentioned in the last paragraph, but also cases where an individual’s preferences are only self-regarding but themselves inconsistent. Universal domain would allow individuals to express any pattern of preferences they like, including one such as xPy, yPz and zPx, i.e. it permits individual inputs to be intransitive[12], and thus it is hardly surprising that we have difficulty producing a transitive social ordering[13]. Moreover, it is a well-known fact that social intransitivity can occur even if individual preferences are themselves transitive[14]. The problem can be resolved, however, if we place further restrictions on the individual orderings, particularly single-peakedness. So long as all agree that the underlying issue can be mapped on a single dimension (e.g. a left-right scale), then agreement is more likely. We need only insist that each voter has some ideal point (which may be central or extreme), and less-prefers points further from that ideal. This excludes anyone who prefers either extreme to a point in the middle[15]; but since such preferences often seem unnatural, it is not intuitively a great cost. Nonetheless, exclusion of non-single-peaked preferences seems motivated only to preserve the possibility of collective judgement, not on a principled basis. There may be cases where such preferences are reasonable – where the issue to be decided is one of expenditure, and an individual might legitimately prefer it to be high or zero (‘do the job properly, or not at all’). Thus it seems that while we should exclude some preferences on the aforementioned moral grounds, we should reject any attempts to restrict individual preferences solely in order to facilitate social choice.

5.5.b Lottery-Voting Assessed

Now we have seen in what sense a universal domain is desirable, we turn to how well lottery-voting satisfies this axiom. If there is room for some issues to be constitutionally protected, then lottery-voting can allow for them to be removed from the agenda. The issue concerns those that are left in the democratic political domain. For example, suppose z is a protected basic right, whereas x and y are matters for democratic decision. Lottery-voting does not put z to the vote, whereas it allows citizens any combination of preferences between x and y (i.e. xPy, xIy or yPx)[16]. Thus it seems that lottery-voting satisfies universal domain fairly easily.

One might, however, worry whether lottery-voting allows voters to express all their preferences. Recall the example where one may want to spend nothing, but where one has a second preference that if the decision is to go ahead a lot is spent. Here, the decision can be broken down into the yes/no question of whether to spend at all, and then the secondary question of how much to spend. It is unclear how this could be resolved by ordinary voting rules – one might vote in several stages, for example, or take a vote between a range of options one of which was zero. It seems that whatever answer is reached will depend as much on how the vote is set up as on the individual preferences, supporting Riker’s contention that electoral outcomes are likely to be either arbitrary or manipulable[17].

While one could employ lottery-voting at each of several stages, e.g. whether to spend at all, and then (if applicable) how much to spend, the obvious way of implementing it is to simply ask each voter for their first preference – which might be no spending, low spending or high spending – and randomly draw one of these. This fits the basic idea of fairness, giving each an equal chance to deciding the vote in favour of their first preference. On the other hand, however, it is clear it will exclude the expression of certain preference profiles. Because one is only asked for one’s first preference, there will be no way of expressing that one ideally wants no spending, but thinks if spending is to happen it should be at a high level. One only gets to express a single preference, and so one will simply vote for no spending and one’s second preference will be ignored[18]. Is this an objectionable exclusion of preference information?

One might have various reasons to think that we should consider all possible preference information: for example, one may think we could reach a compromise that is reasonably acceptable to all[19]. I do not, however, think that not admitting such second preferences is a violation of universal domain. Everyone had a chance to express their first preference, and everyone had a fair chance for that to win the vote. If some people were now allowed to express another second preference, that would be to give them more weight, on account of them having more preferences. We can think of the two issues as being resolved by a single vote, that determines both whether to spend and how much. Everyone is allowed to vote for their ideal outcome, whether that be no spending, low spending or high spending. Supposing the winning vote is one that mandates a set amount of spending, then one’s vote for no spending has already been accounted for, and legitimately defeated. Why, just because one has had one’s vote counted and lost, should one be entitled to another vote to influence the outcome of how much is spent? If it was the latter issue that mattered more to one, one could have voted on it – using one’s vote for either high or low – but ex hypothesi one preferred to vote for no spending. To demand influence also over this second part of the choice is just to demand more say. There is no more reason why a voter should be able to say ‘none, or if not high’ than to let them say ‘high, or if not high’: it would simply be to give some more influence over the ultimate outcome[20].

Thus, in its purest form, it seems lottery-voting satisfies the requirement of universal domain. While the preference information it uses is limited to first preferences, this is true of many voting systems that take only a single vote rather than a list. The axiom is satisfied when and because it is open to voters to express any first preference, e.g. xP[all alternatives], for any x. As I noted in examining the plausibility of the axiom, this will not always be desirable, and we may want to protect certain rights from any democratic decision. This is not, however, an inherent limit of lottery-voting, but simply the result of another choice on constitutional protection. Lottery-voting per se is consistent with either a limited legitimately political domain, or an unrestricted set of allowable first preferences.

[1] E.g.
[2] Arrow (1963) p.28.
[3] Note that Citizen Sovereignty therefore also includes Pareto, which I address next.
[4] Riker (1982) p.117.
[5] Rawls (1999 [1971]) p.27.
[6] Nozick (1974)
[7] Sen ‘Paretian liberal’
[8] Though in this case, of course, they may be able to change the constitution.
[9] This obviously recalls Plato (1992)’s philosopher-rulers, but also Raz’s conception of authority: see Raz (?).
[10] e.g. Fiss
[11] c.f. Dworkin external prefs TRS
[12] See D. Saari (1994) Geometry of Voting p.327.
[13] Imagine a case where everyone had such intransitive preferences. Now it seems we must choose between social transitivity and Pareto.
[14] This ‘paradox of voting’ was discovered by Condorcet, and is discussed in … It can be illustrated by three people (i, j and k) with orderings xPiyPiz, yPjzPjx and zPkxPky.
[15] For the deliberative response, see D. Miller (1992) ‘Deliberative Democracy and Social Choice’ in Political Studies 40 [reprinted in D. Estlund (ed.) (2002) Democracy]. On homogeneity, see G. Mackie (2003) especially pp.47-55.
[16] One might add that any preferences over z (as a matter of private conscience) are also allowed, they are merely ineffective since it is not voted on.
[17] Riker. Which depends on whether the electoral system is already in place, and so produces one outcome unintentionally, or whether it is up to some chairperson to devise an electoral system, in which case they can rig it to favour their preferred outcome.
[18] It would be logically open to vote for high spending, instead, but there would be no point to this if one really did prefer no spending. I will deal with strategic voting later in this chapter. ‘High spending, or don’t bother’ is, of course, another possible – but different – combination of preferences.
[19] Such thoughts motivate Borda counts and approval voting.
[20] One might object that those who vote for no spending only get a say over the former issue (whether to spend), and not over how much; whereas those who vote for either high or low spending de facto also express their opinion that spending should occur. This is not an objection, because the separation into two issues is somewhat artificial: we could simply represent zero as an amount of spending, and therefore only quantitatively, not qualitatively, different. It will be seen that all cast a single vote for what is most important to them: it merely happens that high spending entails a fortiori spending, while a vote for no spending is simply for no spending, and not also for either a high or low amount of such.

Also, if anyone happens to be an expert on Clausewitz, adjudication might be welcome here.

Friday, May 19, 2006


Four quick things of note today:

1) I spoke to my supervisor about the possibility of applying for this lectureship. He seemed quite supportive, which actually surprised me a bit. Still a bit unsure what suspension of status would mean if I were to get the job - particularly accommodation-wise - but I'm not really expecting that at the moment. I think I just have to apply and then wait and see what (if anything) happens. It's too good an opportunity not to at least try for.

2) On the subject of accommodation, the flat ballot happened today and we got the flat we wanted. This is the problem though, were I to not be a student next year I suppose I wouldn't be eligible to it, and Carole from the tutorial office suggested I wouldn't be able to stay as the college were short of accommodation. This seems slightly unfair, because I think having applied I'm now committed to either paying the rent or finding a replacement tenant - I was going through some of these worries last summer, before my funding was confirmed. If I'm committed to paying for the flat, why aren't they committed to letting me live there?

3) I, and the rest of the GCR committee, had lunch with Sir John Krebs (the Jesus College Principal) and his wife. Judging by the lodgings and food, that's a job I'd like...

4) I'd had to cancel my tutorial for the afternoon, because one of my students was ill. I don't know when we'll catch up, given neither of them are around for 9th week... Still, I spent most of the afternoon/evening going through my Nozick notes, including Cohen and my friend Karl's critiques.

Wednesday, May 17, 2006

CL Final

As in 1999, I admit I watched this game with mixed feelings. Generally I’ll support British teams in Europe – and Arsenal are certainly a lot less gut-wrenching to support than the Chavs or Mancs – but there reaches a point where I’m not quite sure I want another British team (and rival) to lift a cup.

If Arsenal had played Barca off the park, then I could probably feel pleased for them. As it was, I was happy Barca equalised, because if they’d lost to a goal after Eboue’s dive it would have left a very sour taste in the mouth. I agree with Henry the ref was poor, but don’t think it cost Arsenal any more. Eboue could easily have picked up a second yellow, and if the advantage law had been harshly applied - as could have been with Cech in last year's semi - Barca’s goal could have stood as well as Lehmann being sent off (though in that case, it would probably have been a yellow - presumably because the scoring chance wasn't actually denied).

Credit to Arsenal though. They played very well with ten men, and still created several breaks as well as looking fairly solid against Barca’s formidable attack. Looks like they did us proud in Europe.

Saturday, May 13, 2006

FA Cup Final

What a match. Of course, as a Liverpool fan, I never doubt our chances of winning unless we’re 4-0 down… I must apologise for doubting West Ham’s ability to play their part in a great final, because they really did. Admittedly, all their goals had a touch of luck (o.g., ‘keeper’s error and a cross that went in), but that’s not to take anything away from their performance. In a match where arguably only one of their big players really stood up, Liverpool never looked the odds-on favourites they’d been billed as.

In fairness, I don’t think Alonso was ever really fit, and that as much as the attention’s of Ashton (who I rate very highly) contributed to a poor game. Him and Kewell both being forced to leave the pitch early through injury hardly helped Liverpool’s cause, with Rafa’s tactical changes thereby forced upon him.

Some people I was watching with criticised Gerrard for coming infield too often, and thereby denying the team width. I agree, but with him scoring two screaming goals (and setting up Cisse’s) to drag us back into the match, one can hardly complain. He really did look like one man carrying the rest of the team on his shoulders…

By extra time, there were players dropping all over from cramp, and few could run. Riise had a good shot, Kromkamp made several runs (though he did little with the ball, one could defend him on the grounds he had few players in support) and Reina was forced into a great save at the death – redeeming himself for earlier mistakes, and recalling those semi finals against Chelsea last year (CL) and this (FA Cup), not to mention Dudek’s save from Shevchenko.

Penalties, of course, are always a lottery (remind me to give you my thoughts on that some time…) but Reina lived up to his reputation by saving three of West Ham’s four kicks, and the cup was ours. Two major trophies in two years is certainly a good return – and the Community Shield means we already have at least three meetings with Chelsea lined up for next season too, of course...

Friday, May 12, 2006

Thursday, May 11, 2006

GCR Meeting

Today was a pretty hectic day. Well, maybe not so bad - Stuart White saw me sunbathing in Second Quad in the afternoon, and commented on the life of a grad student - although in fact I was reading through my notes in preparation for the presentation I gave to Dan Butt's graduate workshop.

Things really kicked off after that, however, with the first GCR meeting of term, and first of the new committee. We had six motions on the agenda, and one further submitted under Any Other Business. The minutes are already available online (Oxford domain only).

Wednesday, May 10, 2006

Otsuka and Punt

Tonight I went to dinner with Mike Otsuka, who'd just been to give a talk to our Political Theory Research Seminar. (More familiar blogger Chris Bertram - of CT fame - was the speaker last week, but owing to a rescheduled time I was unable to attend)

Between this and the Moral Philosophy Seminar, there's a danger I may end up bankrupt if I go to too many dinners at £10-15 a time. Still, it's nice to get more opportunity to meet academics in the field. Mike's someone I've seen at a couple of conferences now, and it seems he recognises my name - he said he even found this post on this blog, via my comment on CT.

Of course, it's also a chance to dine with other Oxford people - including Jerry Cohen (I never knew how keen he was on pepper, or observant of Cowley Road's ethnic eateries) and Claire Chambers, who I discovered is something of a closet Sisters of Mercy fan!

After dinner, I went to join the Oxford punt - that's the local music festival type thing, not to be confused with messing around on the river. (Read my review of the 2002 punt here) I hadn't bought an all-venue pass, but I met my friends Rosemary, Nick L and James in the Cellar.

First band, 100 Bullets Back, were a two piece who seemed to nick their basslines and drum parts from the likes of New Order and Soft Cell (two songs in particular were reminiscent of 'Blue Monday' and 'Tainted Love') and combined this with their own funky-punk approach, including vocals with a megaphone (ah, how Chumbawumba...) Not the most original, but a very 'in' kind of sound at the moment, and a band I'd definitely like to see/hear more of.

Second up were Jabberwock, a local funk type band quite well-known to several members of college. I hadn't seen them before, but I also thought they were pretty good, although less my thing.

The final act was another I'd seen before - The Nailbomb Cults. Actually a one man and his laptop affair, playing gabba/hardcore, with a liberal sprinkling of samples. Too bad 'Disneycore' seems to have been removed from their audiopage, but go check out some of the MP3s and see if they make your ears bleed...

Tuesday, May 09, 2006

Weber Quiz

This week, our regular Political Theory reading group had been planning to branch out somewhat by reading Weber's Politics as a Vocation. Although there were some interesting points toward the end about ethics of conviction vs. ethics of responsibility, and some rhetorical flourishes, I found the reading quite hard. It's quite dry, and predominantly sociological observation rather than argument. Sorry Sarah.

Anyway, it turned out that Tuesday night was pub quiz night at the Old Bookbinders, so we ended up competing in that largely instead, and won a free round of drinks out of it. Too bad we let ourselves down on the music round.

Sunday, May 07, 2006

Happy Birthday Ayelet

Sadly the dodgy weather forecast led to plans of a picnic and possible punting in the Parks being cancelled, but a large gathering a political theorists (plus a few Israelis) gathered on Karl's place for a back garden picnic, and I think it was a great time - despite some complaints about English weather, there was tonnes of food, good company/conversation, and even a bit of volleyball/frisbee to keep us entertained (and feeling young).

Portsmouth 1-3 Liverpool

Too bad that Man Utd's win denied us any chance of 2nd (if only it hadn't been for Rio's late winner in our league meeting...) Still, a satisfactory performance, with three more goals from strikers - Crouch's against a former club and former rival. The result was marred only by failing to keep a clean sheet, and an injury to Alonso making him doubtful for the FA Cup Final.

Saturday, May 06, 2006

Friday, May 05, 2006

Local Ties

I was interested to find, reported in Barbara Goodwin's Justice by Lottery, that settling tied elections randomly is not only an obviously fair solution, but the one actually used in this country. It's even more interesting to find that one local council seat last night was decided by the drawing of straws - or, rather, pencils:

A former mayor of St Albans lost his council seat after an election tie was settled by getting the candidates to pick the longest pencil.

St Albans Tory councillor Keith Stammers lost out to Lib Dem Judith Shardlow after their votes were tied at 1131 each after three recounts.

UPDATE: Discussing this in college, Ellie seemed (mildly) shocked at what happened. 'I thought there'd be some procedure for ties' she said. Well, there is - random selection. Seems fair to me. The question is, if 1,131 votes each calls for a 50/50 chance each, why is it 1,132 votes for one of them would have decided the election definitely?

Also, I'm wondering what reasons there are to prefer drawing straws to tossing a coin. At first, I thought it might be that because it involves a choice on behalf of the candidates it seems less arbitrary. Tossing a coin still involves one calling heads or tails, of course, but that isn't something that's right or wrong.

Tuesday, May 02, 2006


Thanks to Sarah and Glyn to this link to the BBC Magazine, which presents a number of well-known philosophical thought experiments (Thomson's violinist, and the Trolley Problem - which we used for interviews last year, but I guess won't be much good any more!)

Some of the comments almost made me tear my hair out. I'll just mention two:

Thomson's violinist is not the same principle as abortion. If you choose to disconnect yourself you are in essence withdrawing treatment, that is refusing to intervene to save the life of someone who would otherwise die. In an abortion you're choosing to deliberately end the life of someone who would otherwise live.

The foetus is obviously supposed to be not independently viable. Therefore if you 'withdraw' your provision, it will die. Just like the violinist. Someone else does point to a difference:

I would like to point out a problem I have with the direct application of the violinist thought experiment, as presented above, to the case of abortion. In the experiment, if the violinist chooses to stay connected, they need have nothing to do with the violinist once the nine months have elapsed. If a woman is pregnant, and chooses to keep the baby, they will have to bring the baby up - with important consequences for her life, that of the baby, and that of those close to her - or give the baby up for adoption - which again is likely to affect her strongly and will certainly affect the baby.

The natural reading of this is the woman faces further burdens of childcare, beyond the initial 9 months of life support. Accepting the premise (rather than argue the baby allows the woman to live a fulfilled life she couldn't otherwise, or somesuch), then there are further costs to the woman, so if disconnecting the violinist is permissible then so, a fortiori, is abortion. Since the argument is supposed to be favourable to abortion, this isn't really a problem. Abortion will actually be allowed in all cases where disconnecting the violinist is, and maybe some others (because of the higher cost).

Personally, I think it's a shame they didn't discuss Taurek, who discusses one or five cases like the Trolley Problem, and argues fairness requires tossing a coin. No one faces anything worse than death - it isn't worse for any of the five that five die (as opposed to that they die). There is no one who suffers a greater harm of five deaths. Tossing a coin, however, gives everyone a 50% chance of survival.

Also, one other point I owe to Parfit, is one might reasonably think it's better to kill the one in case 3 than case 2. In case 2, that death is (in a sense) gratuitous and unnecessary, because it isn't essential to your plan that there's a person on the other line. In case 3, the fat man's death is necessary, and the essential means to save five. If you were the one killed, would you rather your death did the good of directly saving five, or was merely unfortunate?

For some further thoughts/comments, see Crooked Timber. (But try the survey first, before some insights are given away)

While I'm plugging surveys, my friend Rob offers the chance to plot your views on liberty on his handy matrix. (For now, see the comments thread for my thoughts)

And for those not sick of trolleys, a humorous variant here.

Monday, May 01, 2006


Having done the Magdalen Bridge thing a couple of times – and having stayed up to do so – this year I decided it wasn’t worth it. The sleep deprivation isn’t the kind of thing you need to repeat every year. While I’d recommend anyone who’s only in Oxford for a year to ‘do Mayday’ once, just to say you have (and be part of tradition), the fact is there isn’t much to see or hear.

I did, however, get up at 5:45am and head into college – despite the rain, and need to take a lengthier route up Headington Hill and through the University Parks (due to Magdalen Bridge being closed) - for our champagne and strawberry breakfast, and to hear the college choir. The GCR was packed, and it seems some first years had really entered into the spirit of the event.

In the morning, we went to see Morris dancers, which I think were a new phenomenon to our international students – and while we were there saw a man dressed as a tree. (Emily couldn’t get over this costume – in fact, it seemed quite a babe magnet generally, so may be one to try next year…)

p.s. Happy birthday dad.