### Warwick Paper (Handout)

Tomorrow I'm going to the Warwick graduate conference (which I also attended last year). Here's the handout, which (I hope) gives a good overview of my paper:

3 Using Lotteries to Adjudicate between Groups

(3.4) Starting with Lotteries

Premise: where we must adjudicate between two competing claims to an indivisible good, it is fair to toss a coin. The good is attached to some arbitrary criterion that each party has an equal opportunity of satisfying. Note actual agreement on this procedure is not necessary – what matters is that reasonable people would accept it as fair. I want to ask what to do when there are unequal numbers on either side.

(3.5) Taurek’s Argument for Equal Chances

John Taurek says if we face a choice between one and five people dying, and look at it only from individual points of view, then all we can say is that one outcome is worse for the one and the other worse for the five. Since the one is not required to give up his own life to save the five, Taurek assumes a third party is justified in identifying with this one person, and choosing to save him rather than the five. Further, he claims that if the rescuer wants to be fair, he should toss a coin. The situation in the five-against-one conflict is in no important way different from the one-against-one conflict: tossing a coin gives each a 50% chance of survival.

(3.6) Scanlon’s Objection to Equal Chances

Scanlon accepts the individualist restriction and ban on aggregation, but wants to argue one can justify saving the greater number not on the utilitarian grounds that it is better but on the basis of being fair to each individual. Where there is an extra person on one side he argues she can complain her claim is not duly considered because it has made no difference to how the matter is decided – to still toss a coin is effectively to ignore her presence. Otsuka has criticised this argument as implicitly aggregative, so we need to know in more detail what difference the extra person should make.

(3.7) Scanlon’s Argument for Saving the Greater Number

A vs. B & C

A vs. B, C & D

A & E vs. B, C & D

It seems the only way Scanlon can say that D and E count is hypothetically; for instance, had C not been with B, then D’s presence would have been enough to break the tie with A. So it is not that each person must actually make a difference, because they might already be out-weighed by others, but that had the numbers been otherwise they could have made or broken a tie. Yet if this is all he means, it is not obvious he can reject equal chances. Scanlon cannot find a sense of ‘making a difference’ on which saving the greater number does allow each to make a difference but equal chances do not.

(3.8) The Weighted Lottery: Pooling Chances

A weighted lottery, that proportions chances to each group in accordance with numbers, obviously counts each person equally. As we move through the earlier cases the chances alter from 50/50, to 33/67, to 25/75, to 40/60. The basic idea is that each person has some individual baseline chance (1/n), coupled with the intuition that it is permissible for them to pool these chances. While each officially gets an equal chance on the wheel, the de facto chances of rescue will differ – one in a larger group has more chance of benefiting from others’ good fortune. But if those whose claims don’t conflict share the same slice of the wheel, then we can end up back at tossing a coin.

(3.10) Counting Individuals, Again

When it comes to resolving conflicts of interest democratically we may assume that there are two things people have interests in – one is that their view prevails, but they also have an interest in its prevailing because it is their view, i.e. in their interest being counted and effective. Equal chances may give people fair chances at getting what they want, but it does not respect each person’s preferences because the numbers make no difference.

(3.11) Scanlon’s Argument Against Weighted Lotteries

Scanlon rejects weighted lotteries as: “There is no reason, at this point, to reshuffle the moral deck, by holding a weighted lottery, or an unweighted one” (p.234). But a lottery is only re-shuffling if the deck has already been shuffled to begin with.

(3.12) Prior Randomisation versus Fixed Majorities

Five people are on a ship when it breaks up in a storm. Four manage to get to a lifeboat, while the remaining one is left floating on a piece of wreckage. It is a matter of chance who ends up in each position, so ‘the greater number’ is not a rigid designator. Now a weighted lottery would not only be to “reshuffle the moral deck”, but would diminish everyone’s chances.

Now suppose A goes out to sea alone in a small fishing boat, while B, C, D and E are in the same waters in their larger ship. A knows, when he goes to sea, that he would be the one not saved; would it be unreasonable of him to object to the policy of saving the greater number?

This difference mirrors that between a permanent, fixed majority and a fluid society in which each individual has an equal chance of being in the eventual majority. In the former case, majority rule is fair and optimal. But where groups seem to be defined in advance, the only way to give everyone a chance is to hold a lottery.

(3.13) Proportional Chances versus Proportional Outcomes

Another possibility is compromise on specific policies (results proportional to numbers). We may be able to divide a budget between two projects, but not all decisions are susceptible to compromise or it cannot be arrived at by procedural institutions.

(3.14) Conclusion: Towards Political ApplicationKamm identifies ‘saving the greater number’ with ‘majority-rule’ and speaks not only of saving people but also of satisfaction and preferences. I have argued numbers should make some difference, but need not determine the outcome. The attraction of saving the greater number or majority rule is less obvious when we are dealing with larger numbers with little difference between them, such as 1,001-against-1,000. Weighted lotteries, by proportioning chances, respect numbers: 60% of the people have a 60% chance of victory. As Timmermann says, speaking of the rescue cases, “It is rational for the members of a society not to choose to maximize the probability of being saved. A somewhat lower overall probability is the price they would be willing to pay for their claim’s never being discounted right at the beginning” (p.112).

Labels: academic, lotteries, my life, political theory, thesis

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