Friday, 8 November 2013

The Dark Side of Mathematics

This post starts by discussing the problem of alienation/estrangement of financial counter-parties, and goes on to discuss the role that mathematics has played in this estrangement.

Is default moral?  Noah Smith brought my attention to a post by his colleague Guan Yang reviewing the question of whether default is ethical.  I suspect Noah was prompted to pass this on to me because I had observed that it must be embarrassing for the radical anarchist David Graeber that his argument that "we do not all have to pay our debts" was (almost) being enacted by his ideological opposites associated with the Tea Party advocating US default.

Guan Yang [I assume that Yang has fairly interpreted the sources which I have not read]  lists the main points of the argument, starting with the Deontological point that contracts can be broken, subjects to a payment of compensatory damages: as such default is licit.  Yang suggests this approach is favoured by liberal types as it appears to alleviate misery, however since compensation is due, I cannot see how default can alleviate misery since it does not absolve the borrower from repayment of some sort.   I won't accept an argument that inequality is unjust and so should be corrected by "strategic default" by borrowers, as my mother said and I tell my children: two wrongs don't make a right.

What does absolve the borrower from repaying is if the 'contract' was void, this will be the case if one of the parties (typically the borrower) is not 'competent'.  This is a significant issue in the UK where in 1989 interest rate swaps held by the London Borough of Hammersmith and Fulham were declared ultra vires (beyond the powers) of local government and voided.  UK banks are still hobbled by having to pay compensation for mis-selling insurance products and there are more cases involving small businesses in swaps.  I am not aware of similar cases in the US, whether this is because US banking practice is more conscious of the competence test of US courts expect consumers to be more discerning, I do not know.

The Consequentialist argument is that since default will raise the interest rate across the board, and so an individual's default will damage society as a whole.  Yang summarises the argument as one of social contract, the individual gives up their right to default in exchange for the common benefit of lower borrowing costs.  He associates this approach with Conservatives and libertarians, which is remarkable because it would imply they should adopt similar arguments in other areas, i.e. social insurance, such as Obamacare.  One suspects that Conservatives and libertarians believe rational self-interest dominates coherence here: we can assume wealthy Conservatives suffer when others default, so employ social contract in this case, while contributing to a poor person's healthcare has a similar negative impact on their wealth and so in their rational self-interest they reject social contract arguments.  I believe this sort of muddle is an inevitable consequence of Consequentialist Ethics.

I adopt a Pragmatic/Virtuous approach to solving these sorts of ethical problems.  Virtue Ethics argues that Justice is central to economic performance and so a debt must be repaid, otherwise it is unfair, there is no equality between what was given and what was returned.   But virtues must be Tempered (mixed), and Justice needs to be Tempered with Charity (or benevolence), in particular the lender needs to have a genuine concern for the welfare of the borrower.

This argument is not simply Virtuous, it is Pragmatic, in that it emerges out of practice (in fact the word ethic derives from the Greek for 'habituation').  If you are not convinced of the implicit relevance of Justice and Charity in commerce I suggest you watch The Merchant of Venice as a study of the four natures of love (friendship, family, erotic, benevolent/philia, storge, eros, agape), with Antonio, the Merchant of Venice, personifying Charity/agape and spot the interplay between concepts of love and Justice.

Less abstract is the Quaker attitude to banking.  In the eighteenth and early nineteenth century it was, in the main, Quaker bankers who funded the British Industrial Revolution.  The Quaker approach to lending is captured in the proverb
“Well, Friend”, said the Quaker Banker, “Tell me the answers to these questions so that I may help you in your projects, for you have opportunities: Firstly, how much do you seek to borrow? For how long? And how will you repay the loan plus its interest?" These are the issues all good bankers must explore.
Essential to the process of banking is the question "how will you repay the loan": the lender must understand the borrower.   I would argue that without asking this question the lender cannot establish the competence of the borrower to enter into the loan contract, and so if the lender has not endeavoured to establish this competence, the loan is void.  The question relevant to US policy is how were sub-prime borrowers going to repay the loan and interest? I would argue that it is usurious (i.e. illicit) to see these sub-prime borrowers as profit opportunities if you do not genuinely believe they can re-pay the loan.

I am particularly interested in this idea of enticing people into contracts in order to make profits having just read Jonathan Levy's Freaks of Fortune, a hard to read but fascinating account of the role of life insurance in nineteenth century US society.

In the first half of the book an experience of the abolitionist actuary Elizur Wright in 1844, when he was forty, is described.  Wright was visiting London researching actuarial life tables when he witnessed men standing on an auction block as their life insurance policies were sold.  The men could not afford to keep up the premiums and so would sell the policy to the highest bidder who could afford to pay the premiums until the seller of the policy died, the more destitute the seller of the policy, the higher the price as the buyer would expect not to pay too many premiums until payout.  Wright was shocked to see free-born Englishmen standing on an auction block, as slaves did in the USA, and resolved to legislate that life policies had a surrender value, a price at which the holder could sell the policy back to the insurer if they could not maintain the premium payments.  Calculating the surrender value was not trivial, since premiums were level and did not change through the life of the policy, they were higher than the fair value when the policy holder was young, but lower when they were old.

The mathematics of actuarial science provided objectivity and fairness in calculating the correct premiums and surrender values and helped transform life insurance from speculation on God's will to moral prudence in the face of uncertainty.  In the immediate aftermath of the Civil War (1861-1865), life insurance exploded in the US.  In 1865, life insurers held $85 million in assets, in 1875 (after the disastrous 'Panic of 1873') the figure had quintupled to $435 million (16% per annum growth), reaching  $1,886 million in 1900 (8.8% growth over 35 years).

What caught my interest was that along side this mathematically based industry a 'fraternal' 'counter-movement' emerged.  Insurance is based on the policy holder paying premiums into a fund managed by the insurer, and out of this fund benefits are paid.  The fraternal movement, initiated and exemplified by the Ancient Order of United Workmen, worked on a very different principle.  People would become members of the fraternity on the payment of $1, in the event of a members death the other 1999 members of a fraternal lodge would be 'assessed' for a $1 each, and a $2,000 death benefit would be paid to the dependants of the dead member.

Being a member of a fraternity involved participating in rituals and the fraternal movement was vigorous in preventing any notion of a contractual relationship emerging between member and lodge or the application of actuarial methodologies in the management of the benefit funds.  This was  a popular feature in the aftermath of the Panic and a series of insurance failures of the 1870s.  The aim of the fraternal societies was to replace the corporate insurance principle with a social bond.  Levy explains that the "fraternal society was a decommodified risk community".

When the insurance industry was hauled in front of legislators to defend their actions in  1877, Henry Hyde, the president of the Equitable of New York cast a veil over the industry
There are certain fundamental rules ... which can only be understood by actuaries, and it is impossible for me to go into here
As Levy observes, "Ultimately the certainty was in the science".  Levy also notes that at the time life insurance was seen as being indicative of a progression from society based on "status" to one based on contract.  While scientifically based life insurance provided "certain sums", fraternities only offered "indefinite promises" and a "revolt against multiplication tables".  These arguments seem to ignore the mutual basis of fraternities and the various failures of insures.

While life insurance business was growing rapidly, the 'big three' New York insurers, the Mutual Life, New York Life and the Equitable, introduced tontine policies.  A member of a tontine pays into the fund which has a fixed maturity.  If the member dies before the funds maturity, their share is redistibuted to other members.  Effectively buying a tontine is a bet on your longevity.  It was marketed as a form of financial speculation that offered a benefit to the investor, not just their heirs, but should be hedged with a conventional policy.

Tontines were attractive to insurers because there were fewer restrictions on how the funds in the tontine could be invested-the actuaries could speculate in risky assets. Tontines were dubious, they are fundamentally speculative and explicitly gamble on 'God's providence'.  In 1885 the New York legislators investigated their legality - the response was that  "the only moral/legal obligations that existed were those between two contracting parties" and criticism was unscientific "emotion" that defied actuarial science.

The insurance corporations were becoming behmoth's.  If an insurance policy lapsed (the member stopped paying the premium) the funds became available to the insurer to do as they will.  In 1905 statistics showed that more than half of life policies were lapsing and that the legislated surrender values were essentially worthless.  These funds gave the insurers power on Wall Street and influence with legislators.  Between 1895 and 1905, the Equitable alone provided its Albany (New York state's capital) lobbyist $1.3 million and the impact of this influence was being seen in legislation, such as a New York law that prohibited policyholders demanding an accounting of their tontine funds.

The 1890s also saw a concerted attack on the fraternities.  As early as 1878 the weakness of the fraternal system was exposed when a yellow-fever epidemic menat that the fraternal promises could not be kept in some southern States, but when northern States were asked to support their southern brothers, they refused.  This prompted the creation of a "reserve" fund for the fraternities in the 1880s, which in turn exposed the fraternities to investigation for being un-regulated insurers, how can you have a reserve fund that is not actuarially managed?

My interpretation of the process that Levy describes is that by not holding a reserve fund the fraternities did not become rich on the basis of lapsed policy holders and so could not challenge the legislative power of the insurance companies.  A constellation of forces, the primacy of contract over relationship, profit over benevolence and the authority of mathematics forced the fraternities to morph into insurance corporations. As Levy observes,
the assessment system alone did not mean the societies were benevolent, charitable, institutions, rather than insurance companies.
I am not convinced that this change was a "natural" evolutionary process, survival of the fittest social system.   I believe it came about because the large insurers were able to become powerful by exploiting their policy holders who lapsed their policies, and mathematics was not a neutral player in this process.

I don't think this whole story is of purely historical interest.  Today we are observing the growing phenomenon of peer-to-peer lending and crowdfunding, both phenomena are subject to increasing regulatory scrutiny.  The questions the tale of the fraternal movement raises in my mind is who, exactly, is the regulator protecting? I believe the regulators assume that financial actors must be profit maximisers and therefore need restraining by ex catherdra rules, rather than seeing financial agents as attempting to build a mechanism for communicative action that carries credit in an uncertain environment. In taking this position, incumbents are protected and disruptive initiatives hindered.


  1. "I cannot see how default can alleviate misery since it does not absolve the borrower from repayment of some sort."

    It's actually fairly straightforward. If the borrower has an option to default, then the question is which option is less miserable. If the default option is less miserable, default alleviates misery. Alleviation does not require abolishment.

    "Virtue Ethics argues that Justice is central to economic performance and so a debt must be repaid, otherwise it is unfair, there is no equality between what was given and what was returned."

    Yet as soon as you add interest, you have given up equality as a standard for fairness and thus justice. Likewise, as soon as you incorporate risk to raise the interest rate, you have abandoned equality even farther. When a lender adds in risk, he is adding in the possibility of default (deliberate or otherwise), and the default option is part of the contract. If you cannot assume the contract is fair, you have no way to salvage justice.

  2. I take your point.

    On interest, see my posts on Olivi ( and to see a probabilistic justification of interest in terms of equality see

  3. Most contracts include terms establishing consequences for violating specific provisions of the contract, e.g., forfeiture of collateral. Signing such a contract isn't a promise to repay, it's a promise to repay or accept the consequences of non-repayment. In this light, strategic default hardly seems unethical.

    Going further, a lender might see that circumstances are making the consequences more palatable than primary contract provisions and suggest a renegotiation where the borrower gets some benefit in return for stiffer consequences.

  4. Can debt be forced on one party by another? Clearly this would alter the moral calculus. Paying someone less than subsistence wages, then lending them the the difference they need to survive, (The Company Store) seems to be one way.

    The wealthy have more flexibility in allocating their resources. They thus control the world economic system. They have used this control, over the last thirty years, to increase their share of the nation's/world's wealth. Can they use this ability to control the system to force debt on populations they have already stripped of much of their assets? I see no reason why the stripping of assets cannot be extended to the forcing of debt, though the mechanism seems unclear to me.

    Did Germany force debt on Greece, by pursuing beggar thy neighbor mercantilist policies? Certainly many, perhaps most Greeks, are paying on debt they did not knowingly, or at least with understanding, contract.

    Or consider, lenders wave money, and some borrow, and the extra money drives up the price of goods. Those at subsistence now find themselves below subsistence, and forced to borrow. And the lenders know this will happen...

    1. Debt is constantly "forced on one party by another": the debts that ensue from the inability of the State to operate within its budget constraint are forced onto the tax base, both present and future - even those who explicitly repudiate the right of government to accumulate debt underwritten by the labour of the society on which politicians parasitise.

      And you can't use the 'but they do so on our behalf' nonsense that characterises the Dunning-Kruger-laden central tendency of people who can't do sums. I can say this with absolute certainty, because there is no means of selection of political office-holders that will reliably reflect the 'general will' or 'social preferences' - see Arrow's 1950 Impossibility Theorem, add in the Gibbard-Satterthwait Theorem and Holmström's Theorem, sprinkle on some principal-agent problems and competitive advantage of sociopaths in the "liar's poker" of politics (where you have to fool 38% of the population, max, to form a 'majority government').

      To those who think it's valid to use an 'estimate' of representativeness (of unknown accuracy) as a basis for an entity that claims the right to rain death from the sky on foreign children in 'our' name, and accumulate trillions in debt while doing so: think again. Harder, this time.

  5. Money is "a promise to complete a trade". This is obvious from a simple examination of a trade. A trade has three steps: (1) Negotiation; (2) Promise to trade; (3) Delivery. In simple direct barter steps 2 and 3 happen simultaneously on the spot. Money allows steps (2) and (3) to happen over time and space. Thus, money is simply "a promise to complete a trade".

    Traders "create" money by making trading promises. These they have certified by the Medium of Exchange (MOE) manager (MOEM). He records the details of the trading promise and issues the certificates that then trade freely as items of barter. They "never" lose their value ... any where ... any time.

    Why? Because the MOEM can manage the MOE in such a way that he guarantees INFLATION is zero everywhere all the time. How? Incredibly simple. He just monitors DEFAULTs and collects an equal amount of INTEREST such that INFLATION must be zero according to the relation: INFLATION = DEFAULT - INTEREST. Otherwise, on normal complete of a trade the certificates are returned to the MOEM and he extinguishes them.

    With sophistication, the process becomes an actuarial problem. Responsible traders enjoy zero INTEREST. Deadbeat traders pay "deal killing" INTEREST. And in between these extremes INTEREST is collected by class according to actuarial analysis of propensity to DEFAULT (as insurance actuaries analyze risk).

    Now, knowing this, reread the article. Observe how ridiculous and worthless it is.

    Todd Marshall
    Plantersville, TX

  6. If a loan is taken without intent to pay it back or at some time the borrower, though capable or repaying without causing misery to themselves simply decides not to then it is not moral to default. The borrower is committing a fraud by either not intending to repay or pretending that they can't.
    However, if the lender has offered the borrower terms that they do not or cannot understand, that will extract greater repayments than they believe they will pay and especially if it causes the borrower misery then it is moral to default. The lender is committing a fraud by misleading the borrower about the cost of the loan.
    If the loan simply can't be repaid then morality is irrelevant.


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