Deriving Utilitarianism from First Principles

(revised May 14, May 16 in light of the objection that the argument doesn't have several people's small gains justifying one person's big loss; that characteristics shouldn't matter)

I heard Professor Terence Irwin talk on 'Prudence, morality, and the importance of persons: a dilemma for Sidgwick' yesterday. He said that Sidgwick does a poor job of moving from his two axioms to utilitarianism, which is correct. Even the axioms aren't spelled out very clearly, it seems. Here's a fix-up I thought of.

Axiom 1. Pareto Improvements Are Good. If you can make one person better off without hurting anybody else, do it.

Axiom 2. Impartiality. Whether a change in welfare is good or bad shouldn't depend on the identity of the particular person affected or any personal characteristics. Whether an action that changes welfare by amount A affects person i instead of person j does not affect the action's moral goodness.

Result 3. By A1, if Jones can take an action that increases his welfare by 800 utils, he should do it.

Result 4. Suppose Jones can either do nothing or take the trio of actions T1:
Action X reduces Jones's welfare by 2000 utils.
Action Y1 increases Jones's welfare by 700 utils.
Action Z1 increases Jones's welfare by 500 utils.

By R3, Jones should take the trio of actions T1.

Result 5. Suppose Jones can either do nothing or take the trio of actions T2:
Action X reduces Jones's welfare by 2000 utils.
Action Y2 increases Smith's welfare by 700 utils.
Action Z2 increases Lee's welfare by 500 utils.

By A2 and R4, Jones should take this trio of actions T2.

Result 6. R5 would remain true for any trio of numbers (a,b,c) such that a is less than b+c. Thus, we have utilitarianism.

A possible flaw: Trio T1 has the same identity label for both actions, whereas Trio T2 has a different identity label for each action. Does A2 really require them to be treated in the same way?

Axiom 2 is different from saying that welfare pairs (2,3) and (3,2) are equivalent, and stronger. Even if (2,3) and (3,2) are equivalent, that does not imply that (3,3) and (2,4) are equivalent. Using Axiom 2, though, if start by saying (2,3) and (3,2) are equivalent, then the actions of "give 1 to person 1" and "give 1 to person 2" are equivalent, so we do get the implication that (3,3) and (2,4) are equivalent. Probably we can derive that (x,y) and (y,x) are equivalent too, from Axiom 2, though I don't see how immediately.

Now that I think about it, Axiom 2 is not so different from the contractarian axiom that if a person is willing to accept a gamble, then he should not complain if he is the loser. A contractarian introduces probability, though, and so needs expected utility perhaps-- or at least some comment on what happens to non-expected-utility maximizers.

Co-opting Your Opponent's Issues

Steve Teles talked about a good idea in a conference here last weekend: the idea of going on one's opponent's issue ground in politics and beating him on his own terms. His paper was on Compassionate Conservatism. Here are perhaps other examples. The paradigm is:

"Liberals say X helps Y, but X actually hurts them."

1. X = Immigration, Y = Mexican-Americans

2. X= the minimum wage, Y = poor people

3. X= easy divorce laws, Y = women

4. X= low penalties for crime, Y = blacks

5. X= unions, Y = workers

We need a good name for this tactic. It is not the same as Co-Opting, really, or Issue Stealing

41% of Americans don't pay federal income tax

At a conference today Chric DeMuth of AEI mentioned that a large fraction of Americans pay zero federal income taxes. I googled, and found that a reasonable estimate is 41% of households (from http://www.taxfoundation.org/research/show/1410.html ). That's 43 million tax return (for 2006) out of 136 million total, with an estimated 15 million that don't file tax returns at all.

Mortgage-Backed Securities. See page 4 of Super Future Equities v. Wells Fargo (2006) (3rd amended complaint, N.D. Texas) was posted on Wikipedia and has a good explanation of how mortgage securitization works, and an example of a breach-of-duty dispute. I don't know how accurate the complaint itself is; the defendants reply here.

I'm actually surprised these securities work at all, they require so much trust. A bank sells some mortgages to a trust it creates for the occasion. The trust creates certificates of various risks that get rated from AAA to BBB- that it sells publicly and from BB+ to unrated that it sells privately to various persons. Class A (not *rated* A) certificates get paid in full before any Class B certificates get paid. There is a Servicer, who processes most of the mortgages' payments to the Trust, and a Special Servicer, who processes problem mortgages, ones that are in default or some other specially defined troubled circumstances. Usually about 2% of loans are in the Special Service category. Service fees are naturally much higher for this category.

Northern Rock's trust, Granite, has a prospectus up on the web.

The U.K. and the E.U. Peter Hitchens has a good article, "The dangerous uselessness of 'Euroscepticism'"

The EU isn't going to give up its plan to become a Superstate just because the people of Britain (or anywhere else) vote 'No' in a referendum. Why should it? Such a vote would be silly anyway. You can't be in Europe and not run by Europe any more than you can be in Wormwood Scrubs and not run by Wormwood Scrubs. When we were bamboozled into voting for Common Market entry in 1975 (I voted 'no', but only just) we accepted the Treaty of Rome, which means, and clearly states that its target is 'ever closer union.

This has become more and more unpopular since 1975, as those who are paying attention (or are personally affected) have come to realise that the supposed crackpots of 1975 -Tony Benn and Enoch Powell - were actually quite right. Just as they warned, we were being asked to give away our national independence and this was the most important issue. Those who are dismissed as 'bonkers' almost always do turn out to be right later on, and there is probably a historical study to be done about this.

The obvious conclusion from this is that we should now leave. We were sold a fraudulent prospectus nearly 33 years ago. We have since suffered quite badly as a country, economically and politically - the full cost has been detailed by Christopher Booker and Richard North in a series of books, the best of all being 'The Great Deception' - books largely ignored by many reviewers and journals. We have held back ( quite rightly) from plunging fully into the project, so that we still more or less retain our own currency and our own legal system , our own diplomatic service and our own armed forces, so there is not too much unscrambling to do. And there is a strong, reasoned case for negotiating an amicable departure. If Norway and Switzerland, both far smaller and less globally-connected than we, can negotiate individual terms with the EU, then why can't we?

...Mexico, most certainly not an EU member, has excellent trade terms with the EU. If we want to keep the much-touted rights to live and work in the EU, we no doubt can. Norwegians and Swiss nationals have them. They even have - which we should never agree to - passport-free travel to and from EU countries. To the extent that we wish to trade with the EU, we would be under pressure to agree to EU rules about what we sell. We would no doubt have to pay some sort of contribution to obtain the 'benefits' of EU membership. But we would be able to negotiate this from a position of strength much more advantageous than the one a British prime Minister now finds himself in at Euro-summits. They want our markets far more than we need theirs. We would have no need to need to accept the supremacy over our Parliament of the European Court of Justice at Luxembourg. We would not be obliged to enact EU commission directives as British Acts of Parliament. We could issue our own passports in whatever colour we preferred (I favour a stiff-backed blue booklet myself) and (as does the USA and...Thailand) we could give our own citizens (we might let them become subjects again) greater rights to enter the country than persons from Lithuania or Romania. We could halt the absorption of our independent diplomatic service into the EU's. We could make our own individual trade agreements with the USA, and wouldn't need to get caught in trade wars between Washington and Brussels, as we frequently have been in the past. We could withdraw from the European arrest warrant system, and ignore the new 'Human Rights' commission in Vienna which is shortly to be the fount of political correctness across the EU.

Wicked Borrowers. Professor Mankiw points me to a NY Times article by Tyler Cowen that has lots of good facts, including this:

There has been plenty of talk about “predatory lending,” but “predatory borrowing” may have been the bigger problem. As much as 70 percent of recent early payment defaults had fraudulent misrepresentations on their original loan applications, according to one recent study. The research was done by BasePoint Analytics, which helps banks and lenders identify fraudulent transactions; the study looked at more than three million loans from 1997 to 2006, with a majority from 2005 to 2006. Applications with misrepresentations were also five times as likely to go into default. ...

In other words, many of the people now losing their homes committed fraud.

Charity vs. Investment. Suppose people in Atlantis increase their charity to the poor by 1% of GDP but people in Lemuria increase their investment rate by 1%. In which country will the poor be better off? In the short run, it will be the Atlantians, of course. In the long run, though, Lemuria will grow faster and-- a tricky bit-- the poor will get richer.

Let's suppose the poor do no investment and consume all the charity they receive. two separate cases are (a) when the current non-poor might have poor descendants-- who will inherit some of their investment-- and (b) when they do not. We'll use assumption (b). Let's assume zero taxes, so taxes on investment income play no role. The social discount rate is very important, so let's assume it's zero, leaving it out of the picture. We'll just do some comparisons of the next 200 years. The benefit to the poor from investment might come from (a)increased information production/process innovation, (b) increased product innovation-- new goods, consumer surplus, or (c) an increased marginal product of labor due to the bigger capital stock, and hence higher wages.

I'll ask macro people about this.

The Simple Life. Something worth thinking about are the transactions costs of daily life. Should we make, or buy? Coase (1937) pointed out the importance of this choice. If we make it ourselves, we avoid transactions cost, which are especially onerous if we have to think about the transaction each time. If we buy, we get better division of labor-- in the household, or the firm. Have people thought about this in the context of the household? (surely! both are Old Chicago favorites). Hiring a nanny means determining quality, doing tax forms, etc. It is simpler for the mother not to work. Hiring a plumber is a hassle too. Simpler for father to spend twice as long as the plumber would and do it.

Northern Rock bank nationalization. I posted on Northern Rock some time ago. Now it seems the government is thinking of nationalizing it, because it can't find a private buyer at a good enough price.

Something I proposed in my earlier post was giving small creditors, including depositors, priority in bankruptcy. Suppose a bank had 1 billion in equity finance, 5 billion in bonds, and 10 billion in small deposits. It starts with 16 billion in assets, but the value of the assets goes down to 12 billion. The government steps in (or the bondholders), and the payout would be, under my scheme, 0 to equity, 2 billion to bonds, and the full 10 billion to deposits. If the government steps in reasonably quickly, deposit insurance is redundant, though we could still have it.

I'd like to find out more, but apparently that's not the Northern Rock picture, though. Instead, it was something like this (all numbers are totally imaginary, even in scale-- I use them because concrete numbers are easier to follow than X, Y, Z where X>Z, etc.). The bank had 1 billion in equity finance, 5 billion in overnight loans from other banks, and 10 billion in small deposits. It started with 16 billion in assets, but the value of the assets went down to 12 billion. The other banks noticed first, and refused to re-loan their 5 billion. Instead, Northern Rock sold 3 million in assets and the government lent it 2 billion. Now, Northern Rock is left with 1 billion of equity finance, 2 billion in government loans, 10 billion in deposits, and 9 billion in assets. My scheme would not be any help, because the big creditors have already gotten out their money.

Nor would my scheme have helped even had the government not made the emergency loans. Here is a story for what might have happened then. The bank had 1 billion in equity finance, 5 billion in overnight loans from other banks, and 10 billion in small deposits. It started with 16 billion in assets, but the value of the assets went down to 12 billion. The other banks noticed first, and refused to re-loan their 5 billion. Instead, Northern Rock sold 3 million in assets for 3 billion, and another 8 billion at the fire-sale price of 2 billion to repay the 5 billion in short-term money. Northern Rock would then be left with 1 billion of equity finance, 10 billion in deposits, and 1 billion in assets.

The solution seems simple: don't let banks borrow more than their entire equity capital in the short-term markets. But I don't know banking-- maybe they have to to operate. Later the same day. I found a Reuters page which has the Northern Rock balance sheet info. I expect thsi includes the 20 billion or so pounds of government emergency funding. It looks as if deposits actually *are* a small part of funding, and that the assets would easily pay back the depositors. (I haven't included the asset numbers here because I don't think they're reliable--- on the books they seem to exceed liabilities comfortably, so they must not be written down enough).

 *The bank uses four sources for funding. Balances for each
segment were:

 --Retail 24.4 billion pounds (23.2 percent of total)

 --Securitisation 45.7 billion pounds (43.6 percent)

 --Non-retail 26.7 billion pounds (25.5 percent)

 --Covered bonds 8.1 billion pounds (7.7 percent).

 *The bank had total customer account liabilities of 30.1
billion pounds, consisting of retail balances of 24.4 billion
and other customer accounts of 5.8 billion. ...
 

 

 *Bank liabilities totalled 110.1 billion pounds, including:

 --Customer accounts 30.1 billion pounds

 --Debt securities in issue 71 billion pounds

 --Deposits by banks 3.7 billion pounds

 --Derivative financial instruments 2.9 billion pounds.

Part-Whole Bias--The Embedding Effect. ``Contingent valuation'' is a survey technique used in cost-benefit analysis for public goods. These goods are not traded in the market, so market prices cannot be used to value them. Instead, the analyst asks a sample of people how much they are willing to pay for the public good, which is often some environmental good such as wildlife preservation. Surveys are notoriously bad at eliciting true valuations, and the contingent valuation method has been much criticized. Diamond \& Hausman (1994) survey some of these criticisms, including that of ``part-whole bias'', or ``the embedding effect''. The clearest example is from a study by Desvouges, Johnson, Dunford, Hudson, Wilson \& Boyle (1993) which asked some people how much they would pay to stop the killing of 2,000 birds, some people 20,000, and some people 200, 000. The answers were all roughly the same, even though presumably it is worth spending more to save 200,000 birds than to save 2,000. Diamond and Hausman suggest that respondents were not really saying how much they valued birds, but were giving themselves a good feeling by donating, even if only in the abstract, a sum towards wildlife preservation (the ``warm glow effect'' of Andreoni (1989)). People do not view saving 200,000 birds as the addition of one-hundred 2000-bird projects. Similarly, Kemp \& Maxwell (1993) asked one group of people how much they would pay to reduce the risk of oil spills off the coast of Alaska, and found an average valuation of \$85. They asked a different group how much they would pay for a broad range of government programs, and then asked that group to divide and subdivide their willingness to pay for the various items in the package. By the time they broke it down to reducing the risk of oil spills off the coast of Alaska, the value was down to \$0.29. Asking about the oil spills separately gives it a much higher value; the whole is worth more than the sum of the parts. (For a a wide variety of other contingent valuation studies see Frederick \& Fischhoff (1998)). Surveys have their own special problems, but the embedding effect can arise in real decisionmaking too, as Bateman, Munro, Rhodes, Starmer \& Sugden (1997) found in experiments in which subjects traded restaurant vouchers. This should not be surprising. Many people devote considerable effort to budgeting their spending, and such effort would be unnecessary if we were endowed with enough brainpower to costlessly link every consumption decision to every other actual and potential one. Naturally, if we are reminded of other items we could buy-- or told of options that are entirely new to us-- that affects our decisions.

An Example Where Imperfect Message Transmission Helps. Myerson has an example on page 842 of this Handbook chapter with two possible states and three actions where communication fails if the messages always gets through, but helps some if they only get through half the time. Suppose the Sender knows the state of the world is A orB, with equal probability. The Receiver can choose X, Y, or Z. If the state is A, the Sender-Receiver payoffs are (2,3), (0,2), (-1,0). If the state is B, the Sender-Receiver payoffs are (1,0), (2,2), (0,3). If messages always get through, the Sender's message is irrelevant and the Receiver chooses Y, for a an expected payoff of 2 instead of 1.5 or 1.5. If the message is sent by a pigeon who gets shot down on the way with probability .5, then an equilibrium (not unique) is for the Sender to send the pigeon if the state is A but not if it is B and for the Receiver to choose X if the pigeon arrives and Y otherwise. Both players get higher expected payoffs as a result of using the "noisy" pigeon. See the link for more explanation.

Progressive Taxation. Should tax rates be higher on the wealthy than on the poor? A well-known reason is that the marginal utility of income is lower for the rich, so redistributing wealth to the poor could raise total utility. Another reason might be to get the amount of government spending right. A rich person would be willing to give up more of his income than a poor person for a typical good,including perhaps for a typical public good such as defense spending. The rich man might be willing to pay 20,000 dollars for a new mortar whereas each of two poor men would pay only 3,000 dollars. If the mortar costs 15,000 dollars, a tax system whereby each person paid equal amounts of 5,000 each would result in the poor men voting against the mortar. Both the rich man and the poor men would prefer a tax system in which the poor men paid 1,000 each and the rich man paid 13,000, because everyone would vote for the mortar and everyone would get positive surplus. Not just fairness, but correct incentives for voting require that tax rates match with desired spending. This is probably not a new idea, but I'll note it here anyway.

The Stylized Facts of Entry. I was just reading Paul Geroski's "What do we know about entry?" International Journal of Industrial Organization, 1995. It's a well-written survey of empirical patterns like the following:

Stylized fact 2. Although there is a very large cross-section variation in entry, differences in entry between industries do not persist for very long. In fact, most of the total variation in entry across industries and over time is 'within' industry variation rather than 'between' industry variation. Stylized fact 3. Entry and exit rates are highly positively correlated, and net entry rates and penetration are modest fractions of gross entry rates and penetration.

Downward Sloping Demand Curves for Stocks. Marzena Rostek presented "Frequent Trading and Price Impact in Thin Markets," (with Marek Weretka)today at Nuffield. It's a simple approach to downward-sloping demands for assets. Suppose there are a number of traders with CARA utility functions and stock returns are normal, so the traders care only about mean and variance. Each trader holds some portfolio of stocks. He would like to diversify, but if he puts some of his stock on the market, he has market power and will push down the price, since other people will have to be paid to hold more of that kind of risk. As a result, he will hold back some of the stock rather than diversify fully. Also, in way I do not fully understand this can explain splitting a trade up across periods. It is not for informational reasons-- there is full information in this model-- but because if I try to trade more of my stock in a period, I will drive down the price, keeping other people's quantity offered constant.

Price Discrimination Terminology. Last week at the I.O. workshop someone had a good idea for replacing the old 1st, 2nd, 3rd degree price discrimination terminology. Exogenous-feature price discrimination is based on things the buyer can't change that the seller observes, such as his age. Endogenous-feature price discrimination is based on things the buyer can change, such as the quantity he buys or the quality he buys.

A Model of Probabilistic Rules for Project Acceptance. This is inspired by a recent working paper by Vickers and Armstrong. Project i has payoff (Ui,Vi) to agent and principal and is feasible with probability theta_i. Both players must agree to implement a project; otherwise they get (0,0). They can agree to one project at most. Only the agent observes which projects are available. He can keep silent or he can truthfully reveal the (U,V) of a project, but he cannot lie. (Click here to read more.)

First, the principal commits to an accept/reject rule.

Second, the agent proposes a project if he wishes.

Third, if an acceptable project was proposed, it is implemented.

Project A: (9,10), probability = 1.

Project B: (7,100), probability = .7.

Rule Alpha: Accept the proposed project if V < 8.

Rule Beta (best) Accept the proposed project for sure if V < 8. Accept with probability .5 if V > 8.

Rule Gamma (worst): Accept any proposed project. There are two possible states of the world. With probability .7, both A and B are feasible; with probability .3 only A is. Under Rule Alpha, the agent will propose either B or nothing. The principal's expected payoff is .7(100) + 0 = 70. Under Rule Beta, the agent will propose B if it is feasible and A otherwise. The principal's expected payoff is .7(100) + .3(.5)(10) = 71.5. Under Rule Gamma, the agent will propose A. The principal's expected payoff is 1. What's happening is that since the principal can't use cash to reward a high-V proposal (or punish a low-V one), he commits to destroying some of the value of a low-V proposal. Could we change the example to have probability .001 of every other project on the convex set containing A and B?