Decisions, decisions

Of all the more intractable problems I have encountered, Brexit is top of the list. Every time we think we have found a way forward, reality intervenes to cast us back to square one. It strikes me that one reason for this is that we are thinking about the problem in a binary way, which is inappropriate given the complexity of the issue. As it is conventionally presented in the media – and indeed in parliament – Brexit is a simple case of in or out. The prime minister’s ill-judged attack on MPs last week was a product of this kind of simplistic thinking. But it is wrong. There is a cost associated with each choice and the optimal strategy is to choose the one with the lowest costs. It is thus wrong to think simply of “in” or “out.” The real choice has always ever been between “in” and “what kind of out?”

Rather than trying to solve the problem by looking forward, we can use the method of backward induction which begins by looking at the end point and working back to determine the path necessary to get there. One of the great advantages of this approach is that it allows us to abstract from a lot of the political noise surrounding the current debate. Thus, to answer the question of how to leave the EU with an agreement that minimises economic costs to the UK, we can work out the sequence of events designed to get us to that point. By sequentially going through the outcomes, we end up gradually eliminating all the impossible options until only the possible ones remain. None of them accord with the plans put forward by the most fervent Brexit supporters.

But whilst this is an approach which allows us to look at desired outcomes, methods of voter choice help us to assess how we actually arrive at our choices, however unlikely they may be. Consider a system of single transferable votes in which 650 MPs face four options, A, B, C and D. Suppose they rank their preferences from 1 to 4. If no option commands a majority, the lowest-ranked first choice is eliminated from the ballot and the remainder are subject to a vote in the next round. The attached chart shows the sequence of how this might pan out.

In the first round, options A and D have an equally low number of first preferences but A is eliminated because it has a smaller number of second preferences. In the second round, D again scrapes through on the basis of having more second round votes than C and in the final round it ends up on top because more voters switched their allegiance to D than B, despite the fact that D was never a first choice winner in either of the first two rounds. Imagine now that option D is either a hard Brexit or revocation of Article 50. Although these are not plausible outcomes today, such a voting system demonstrates how they could end up as being the favoured choice depending what other choices are available.

An alternative voting system is the Condorcet method which attempts to force a decision by holding a series of one-on-one votes to determine whether there is one preference that comes out on top. In our example, we thus run six votes (A vs B); (A vs C); (A vs D); (B vs C); (B vs D) and (C vs D). If preferences are transitive (i.e. if A is preferred to B and B is preferred to C, then A must be preferred to C), it is possible to derive a winner. But if they are non-transitive it is not. Imagine, for example, the case where MPs are asked to choose between accepting the Withdrawal Agreement and revoking Article 50 and opt for the former. In a second vote, MPs prefer accepting the Withdrawal Agreement over a hard Brexit but in a third vote they express a preference for a hard Brexit over revoking Article 50. It is thus impossible to derive a series of ordinal preferences. This is known as the Condorcet paradox which we can liken to the game rock-paper-scissors, to which there is no obvious solution.

The work of Nobel Laureate Kenneth Arrow highlighted the problems involved in arriving at optimal choices. He gave his name to Arrow’s impossibility theorem which suggests that when there are three or more options, no ranked voting system can convert the ranked preferences of each individual into an overall ranking which meets a number of specific criteria. Perhaps the most important of these is that one person or group of people cannot be made better off without making others worse off (the Pareto criterion). This is an accurate description of where we are in the Brexit debate given the sentiments expressed on the streets of London at the weekend.

Continuing to put a series of votes to parliament, none of which commands a majority, can ever be guaranteed to find a resolution to the Brexit problem. The very fact that the electoral split in favour of leaving the EU was not much more than 50-50 ought to make us question why MPs can find a resolution when the electorate could not find a solution to the Brexit impossibility conundrum. The government’s approach has been to treat the outcome as a zero-sum game. But as the estimated one million people marching through London at the weekend highlighted, this approach is far from satisfactory. The only resolution to the problem is to buy more time: Kick the can down the road in the hope that society is able to agree on an acceptable compromise. Theresa May gained only an additional three weeks. It’s not enough!

Thinking out of the box

Some months ago I came across a book entitled Radical Markets: Uprooting capitalism and Democracy for a Just Society by Eric Posner and Glen Weyl which proposes that in order to organise markets for the good of everyone, we should be less concerned about curbing market power than giving them free rein to operate. Given that one of the motivations for this blog in the first place was to highlight that markets do not always deliver optimal social outcomes, in contrast to much of the conventional thinking amongst policymakers, the ideas in this book caught my eye. Admittedly, most of them are bonkers and will never be implemented, but at the very least the authors force us to look more closely at the ills within our current economic system. On the basis that if you can diagnose the problems you might be able to find a cure, this is a useful service.

One of Posner and Weyl’s key ideas is that property rights confer a monopoly status that prevents markets from operating properly.  Take the example of land: A landowner can extract a very high price from someone who wants to put the plot to a more productive use. They pose the question whether it is socially just that the landowner can extract rent at the expense of wider society. Their solution to this problem is brilliantly ingenious, albeit impractical. All members of society assign a value to each and every asset that they own and are taxed on the basis of their declared wealth. But the twist is that if someone offers to buy the asset at the value which the owner declares, they are legally obliged to sell it.

In a world of perfect information, asset holders would be able to value their assets at a sufficiently low price to minimise their tax bill but high enough to deter potential buyers. But because we do not inhabit such a world many asset holders will overvalue their assets, in which case society benefits from the additional tax revenue that results. Similarly, many will undervalue their assets which will allow wealth to be redistributed throughout the economy. As an intellectual thought experiment, I was very much taken by the idea. Obviously it would never work in practice because the ultra-rich would simply acquire the assets of the less well-off and we would end up with more concentrated ownership of wealth. But at a time when there is evidence of increased industrial concentration, with a smaller number of firms accounting for a rising proportion of sales in most economic sectors (think Amazon or Apple), this is brave attempt to force the concentration problem onto the agenda.

The authors also propose solutions to the problem inherent in democratic systems whereby the rights of minorities have to be protected, but equally minority interest groups cannot be allowed to block the progress of a wider agenda. Posner and Weyl use the area of environmental regulation as an example but we might even apply it to the Brexit problem, where the actions of the DUP and the ERG have thwarted plans to move things forward. Posner and Weyl’s solution is to abandon the principle of one person one vote and instead give individuals a fixed supply of credits which means that if they expend them on one issue, their blocking power in other areas is correspondingly reduced. In the authors’ words, “a vote can tell you only whether a person prefers one outcome to another, but not how much the person prefers the outcome … we need a way of determining whether the intense preferences of the minority outweigh the weak preferences of the majority.”

On a day when the UK government has issued its immigration White Paper which I found a profoundly depressing and economically illiterate document, based as it is on pulling up the drawbridge, it should come as no surprise that Posner and Weyl weigh into this subject. Their analysis on this area is pretty weak but it boils down to the idea that citizens should be allowed to sell a visa to an immigrant  worker, to whom they provide financial support until such times as the immigrant is able to stand on their own two feet. The rationale is that society benefits from the additional income which flows from immigration, though I struggle to see why those who are not prepared to sponsor immigrant workers should be allowed to free-ride on the additionally generated income.

But mad as many of the proposals are, and unlikely as they are to be implemented, the authors at least have a go at identifying many of the problems which have exercised voters across the western world. The question of whether society could or should accept the undermining of individual property is more troublesome. However, many of the cases highlighted in the book demonstrate that in theory, individuals can better express their preferences by giving up their rights. In a year when The Economist has called for the liberal agenda of free trade and free markets to be redefined in a bid to enhance living standards, the book is suitably thought provoking.

As a final thought, until 1917 just four major countries permitted universal suffrage and it was not until 1971 that all cantons in an enlightened country such as Switzerland allowed women to vote. What was once unthinkable is now commonplace. Just because we cannot imagine how some of Posner and Weyl’s solutions might operate does not mean that they should be dismissed out of hand.