Tuesday, October 27, 2009

Drink Driving Limits and Cost/Benefit Analysis

The recent debate surrounding Minister for Transport Noel Dempsey's proposals to reduce the legal alcohol limit for drivers from 80mg to 50mg of alcohol per 100ml of blood provides an interesting insight on the economist's tool of Cost/Benefit Analysis.

On one side we have the Minister arguing that the benefits of the measure will be the lives saved as a result of the new law. On the other side we have TDs such as Mattie McGrath (FF, South Tipperary) suggesting that the costs of the new measure will be increased isolation of people, especially older people, in rural Ireland.

As a decision-making tool the decision rule in a Cost/Benefit Analysis is relatively simple. Once all the relevant costs and benefits have been monetised an action should be taken if the value of the benefits exceeds the value of the costs. That is, the action or policy results in a net benefit or gain to society.

The current drink driving debate highlights one the major difficulties in appropriately undertaking a cost/benefit analysis: monetising the benefits. The proposals put a reduction in deaths and injuries from road accidents versus increased isolation of the rural community as the opposing costs and benefits. These are factors that have no direct monetary value and so must be valued indirectly if a true cost/benefit comparison is to be made.

Each side will also seek to increase the values supporting their view and reduce the values that should be placed on the factors on the opposite side. For example if we consider the public mutterings of those against the measures we can see that they have argued that the benefits should be lower and the costs of higher.

They have suggested that the true figure for the reduction in road deaths is lower than what is the Minister has presented. Mattie McGrath has also argued that a drink or two has a relaxing effect on people and can make some people better drivers, a loss which increases the costs of the measure. On an interview on Newstalk he said, "some people, if drink is such a sedative, it can make people who are jumpy on the road, or nervous, be more relaxed".

Looking at those backing the measure European Transport Safety Council director Antonio Avenoso has said that:
"...saving lives was more important than any perceived threat to rural social life.

We should also not forget that rural communities have also been shattered and
devastated by lives lost, by people who have brain damage and by people who have
long-standing injuries because of traffic accidents due to drink driving."
The Road Safety Authority has gone a step further and half done one half a Cost/Benefit Analysis. They have argued that the benefits of the new regulations can be valued at €70 million per year. This is as a result of a reduction in accidents leading to 10 fewer deaths, 100 fewer injuries and less damage caused. Cliona Murphy of Alcohol Action Ireland has argued that the costs of imposing the new rules should be zero.
"With regard to all alcohol-related issues, this is probably as clear-cut as it gets. I'm at a loss to understand why a person's right to have a pint and drive overrides my right to drive on roads free from alcohol."
Working out who is right or otherwise is a complex task and not the issue here. The aim here is to merely highlight the difficulties that arise when trying to undertake a cost/benefit analysis when monetising the factors cannot be done directly.

To finish we will take one claim and see if it stands up to scrutiny - the claim by the RSA that this measure will save 10 lives per year.

The key report on this issue is based on research done by Dr Declan Bedford et al for the HSE. The report which covers the three year period 2003 to 20055 is available here and a recent slideshow presentation of the report is available here.

According to the report 18 drivers were killed in the three year period who had a blood alcohol content of between 50mg and 80mg per 100 ml of blood. This is legal under current law but would be illegal if the proposed measures are introduced. This gives an average of six deaths per year. Four below the figure of ten as promoted by the RSA. Can we get there?

Thus far we have only included drivers. Other fatalities on the road occur among pedestrians/cyclists and passengers. Using figures in the report it is possible to suggest that about 1.5 pedestrian/cyclist deaths per year could be avoided if the new rules were implemented. This is found by multiplying the following numbers. Proportion of accidents in which driver alcohol is an issue (31%), proportion of these accidents in which blood alcohol is between 50mg and 80mg per 100ml (8%) and average number of pedestrian/cyclists deaths per year where pedestrian/cyclist alcohol is not an issue (57). A similar analysis for passenger deaths suggest that there would be two less passenger deaths per year if the blood alcohol limit was reduced to 50mg.

This puts the total number of deaths reduced at six plus one and a half plus two giving a total of 9.5. We're not too far off the quoted figure ten less deaths per annum. Can we find another 0.5?

In 35% of driver deaths no blood alcohol readings were taken or were not available to the researchers. It is likely that in some proportion of these cases alcohol was an issue but the data is not available to reveal this. In many cases tests may not be undertaken because there are clear reasons to suggest that such a test is unnecessary. Still, there are bound to have been a (small?) number of cases where data is not available but driver blood alcohol of between 50mg to 80mg per 100ml is present. We can assume that these cases will result in 0.5 road deaths per year.

We now have support for the RSA claim of a reduction of 10 road deaths per year that forms part of the €70 million per annum benefit if the new measures are introduced.

Is there an issue here?

YES! The RSA analysis is based on the assumption that the reduction in the limits will result in the elimination of ALL deaths that were a result of driver blood alcohol of between 50mg and 80mg. All of them!

If this is to true then it must be that there are no deaths above the current 80 mg limit. Of course not. 80% of killed drivers with alcohol had blood alcohol above 80mg. Of those with alcohol the average reading was 88.9mg per 100 ml.

How many deaths will be avoided if the blood alcohol limit is reduced to 50mg? In fact, the first question should be "will any deaths be avoided?". The answer to this question is probably "yes" but the number is undoubtedly less than ten, maybe even substantially so.

Do I know the answer? No. Just be careful what you read when it comes to pronouncements on a cost/benefit analysis!

Wednesday, October 21, 2009

Split or Steal?

Jasper Carrot teaches Game Theory.

The TV game show Goldenballs concludes with two contestants facing off in a situation that is a variation of The Prisoners' Dilemma. The main workings of the early part of the game are unimportant, what is of interest here is the final round.

Each contestant chooses a ball, either Split, which means they try and split the jackpot with the other contestant or Steal which means they try and steal the entire jackpot for themselves. There are three outcomes as follows:

  • Both players choose Split: The winnings are split equally between them.
  • One player chooses Steal, the other Split: The player who played 'steal' gets all the money.
  • Both players choose Steal: No-one gets any money.

The conclusion of one such episode is shown in the following clip.

The problem is the same as The Prisoner’s Dilemma except it is not quite as pure. This is a one shot game, but the players are in the same room, in fact, they’re looking right at each other, their friends and family are watching and they are given the opportunity to convince the other person of their intention to either Split or Steal. There is more at stake than some money, their reputation amongst all people for one. On top of all of this they have been playing a game for the past half hour and have had the chance to betray each other already.

The similarities with the Prisoner's Dilemma are:

  1. It is a game of cooperation (share) or defection (steal).
  2. Decisions are made simultaneously.
  3. It is a one shot game

The major differences are:

  1. This is a zero-sum game.
  2. The players can communicate.
  3. Steal (defect) is only a weakly dominant strategy

Here is some analysis of the decisions involved:

The worst outcome in this game is for the players to both choose ‘steal’ as that would mean no one wins the jackpot. All other scenarios mean the full jackpot is given to at least one of the players. At initial inspection it may appear that the jackpot will be given out ¾ times and no jackpot a ¼ of the time. But the interesting thing with this game is that assuming all players behave rationally the outcome will actually always be that no one wins the jackpot (i.e. two steals).

If you put yourself in the position as a player, you can see how this works. There are two possible options that your opponent can choose (‘steal’ or ‘split’).

Take scenario 1 where your opponent chooses ‘split’. Here if you choose ‘split’ you will get half the jackpot, if you choose ‘steal’ you will get the entire jackpot. So obviously any rational person will choose ‘steal’ as this will maximise your winnings.

Take scenario 2 where your opponent chooses ‘steal’, in this scenario it is irrelevant whether you choose ‘steal’ or ‘split’ because either way you will get nothing. So given the scenario 2 decision is irrelevant (as ‘steal’ and ‘split’ both result in 0) your decision should be based purely on scenario 1 where it has already been illustrated that any rational person will choose ‘steal’.

So the optimum strategy for any player is ‘steal’! Of course the problem with this is that your opponent has the same options as you and therefore will pick ‘steal’ which means the game ends in two ‘steals’. So going back to the game show assuming that all participants are rational human beings the first 55 minutes of the show are irrelevant because whatever the jackpot ends up being the result of the game will always end up with no one wining anything.

So what actually happens when people are faced with this choice on the show. The show is currently half way through its sixth series and in the five and a half series to date 253 episodes have been broadcast. Data on the 40 episodes in the first series are available here. This gives us a sample of 80 people who were presented with the Goldenballs Dilemma. The average jackpot competed for in the 40 episodes was £12,975.76.

Even though we have shown that 'steal' is the weakly dominant strategy of the 80 contestants, 42 of them chose 'split', or just over 52%, with the other 38 contestants obviously choosing 'steal'.

There were 12 episodes in which both contestants chose 'split' and the jackpot was divided. The average split jackpot was £9,245.49. That leaves 18 people choosing 'split' who had 'steal' played against them and ended up with nothing. The average stolen jackpot was £17,807.14. In the remaining ten episodes both contestants choose 'steal' and the jackpot was lost. The average lost jackpot was £8,742.25.

So the outcomes were:

Both players choose Split:- 12 episodes (30%) Average jackpot = £9,256.49
One player chooses Steal, the other Split:- 18 episodes (45%) Average jackpot = £17,807.14
Both players choose Steal:- 10 episodes (25%) Average jackpot = £8,742.45