Tuesday, 20 December 2016

How The Relative Misleads

Qualities in life - be they ability, money, looks - have both an absolute value and a relative value. Let’s take wealth; your absolute wealth is the intrinsic gains and losses that occur in your own finances, whereas your relative wealth is how those gains and losses are perceived in relation to others.

Everyone can appreciate the changes in their own absolute wealth. If your first effort as a novelist earns you £250,000 you'll be happy. If it earns you £350,000 you'll be happier still. Sometimes, though, your views on absolute wealth change when presented with different comparisons related to relative wealth. For example, suppose you were looking for the balance between financial rewards and critical acclaim - and for simplicity’s sake let's suppose you're never going to write another novel again, meaning that critical acclaim or critical derogation won't affect future publishing potential. Consider the following choice:

Scenario 1
Option A) £350,000 and worldwide critical derogation
Option B) £250,000 and worldwide critical acclaim 

In the above scenario you would choose option B if your value of critical acclaim (and the corollary, your aversion to derogation) exceeds £100,000. If your value of critical acclaim is less than the difference between A and B then you’d choose option A. Let’s suppose from now on that you value critical acclaim at £35,000, you would opt for option A in the above scenario.

Now let's look at two more different scenarios, where you value critical acclaim at £35,000.  Consider the following choice:

Scenario 2
Option A) £375,000 and no critical acclaim
Option B) £350,000 and critical acclaim

In scenario 2 you should choose B because the value of the sum earned (£350,000) plus the value of critical acclaim to you (£35,000) amounts to £385,000, making it more favourable than option A, which at £375,000 is worth £10,000 less. Most people who valued critical acclaim at £35,000 would, I suspect, choose option B.

But suppose you still valued critical acclaim at £35,000 but were given a third scenario:

Scenario 3
Option A) £50,000 and no critical acclaim
Option B) £25,000 and critical acclaim

In scenario 3 your decision should be no different to scenario 2. Nothing has changed in absolute terms: in scenario 3 the sum of your valuation of critical acclaim (£35,000) and the earnings (£25,000) amount to £10,000 more than the option A (£50,000). But I suspect you'd be much less likely to choose option B in scenario 3 because your concern for critical acclaim would reduce your cash earnings by 50%, whereas in scenario 2 it would reduce your cash earnings by just 6.7%.

That is to say, in relative terms the difference between £25,000 in scenario 2 (6.7%) is a lot less painful than the difference between £25,000 in scenario 3 (50%) even though the absolute value doesn't change.

Clearly this is understandable; a 50% increase from £25,000 or £50,000 can change your life by a very great amount, whereas if you've obtained the life-changing amount of £350,000, then that extra £25,000 increase to £375,000 changes your life by considerably less. This is called the law of diminishing marginal utility, where the first unit of consumption of a good or service brings about greater utility than the second unit of consumption, with diminution continuing with more and more units.

In the above scenario your relative considerations were not against the earnings of other authors, they were considerations related to the trade off between earnings and critical acclaim. Quite often, though, the earnings of others is a big factor in people’s decisions. Let’s consider a different example, which shows how much emphasis people place on relative value over absolute value. If given the following choice:

Option A) You increase your earnings by £12,000 per year, and all your same-sex friends increase theirs by £15,000 per year

Option B) You increase your earnings by £11,000 per year, and all your same-sex friends increase theirs by £8,000 per year

Surprisingly, a lot of people would choose option B, because their relative wealth in comparison to their same-sex friends is more important to them than an increase of £1,000 in their absolute wealth if their friends' absolute wealth increases by more.

I think this is irrational. £1,000 is still as valuable to you in monetary terms irrespective of whether your friends increase their absolute wealth by £8,000 or £15,000. Only if your social status is more valuable to you than £1000 should you choose option B - but I think it'd be a sorry thing if you valued social status that much.

Here's another example - this time an example of how humans are irrational when faced with different numbers.

Scenario 1
You are about to buy a specialised pair of welding gloves for £60 in Lewisham, when an app pops up on your phone telling you that at a shop in the centre of London the welding gloves are £30 cheaper (that's a £30 saving even after Tube costs and additional time have been factored in as well).

If you asked 1000 people if they would go into London to make that saving, many would, as it's a 50% discount. Now here's a variation on that question.

Scenario 2
You are about to buy a brand new Nissan Micra for £1499 in Lewisham - but in the centre of London the same car company has the exact same car that will cost you £1469 (that's also a saving of £30, again with Tube fare and additional time factored in).

Suppose every other detail is the same except the relative nature of the £30 saving, I'll wager that if you asked 1000 people whether they'd now bother to head into the centre of London to save £30 on a Nissan Micra, most would say no.

Given the relative infrequency with which we buy a new car, there should be no difference in the two options - if you value the £30 saving on the first product you should value it on the second product too - but almost no one does, because relative to £1499 a £30 saving is nothing like a saving relative to £60. 

After putting questions like this out there for public consideration I've also found that people are often irrationally more cautious with large numbers than small numbers, even if the same probability occurs in both situations. For example, suppose I gave the average person the following scenario:

Option A) You have a big bag with 1 black ball and 999 white balls inside. You get to pull one ball out; if it's black you die, if it's white you get £1 million pounds.

In that scenario most people would feel pretty confident and probably take up the offer. Suppose now I gave the average person this scenario:

Option B) You have a very big bag with 1000 black balls inside and 999,000 white balls inside. You get to pull one ball out; if it's black you die, if it's white you get £1 million pounds.

Regarding Option B, my results overwhelmingly show that people would be more cautious than with Option A even though the probability is the same. In fact, I fancy that if you gave 1000 people Option A, got them to choose to take part or not, then wiped their memories of Option A and proceeded to give them Option B, a large number would give a different answer.

When it comes to things like wealth inequality in the world, humans still tend to be much more interested in relative wealth than absolute wealth. The trouble is, unless this is done sensibly it causes people to forget arithmetic and to think irrationally. My advice is that unless there is a jolly good reason for thinking relatively, people should get into the habit of thinking in terms of absolute gains and losses, and not be anchored by how those absolute gains measure relative to other people's absolute gains.