Here's how the authors frame it:

Since a “square deal” amounts to assuming that all possible hands are dealt with the same probability, we must interpret the drawing of the above number s as a chance move, each one of the possible values s = 1, • • • , S having the same probability 1/S. Thus the game begins with two chance moves: The drawing of the number s for player 1 and for player 2, which we denote by s₁ and s₂. 19.1.2

Essentially, in two player poker, you could distribute cards labelled 1 - 100 and have people bet / bluff on whether their number is higher or lower than their opponents. That might not be a fun game - but it is a useful toy example for thinking about formal rules for a game.

It is sometimes helpful for us to reduce the complexities of the real world into simple examples. It allows us to examine our base assumptions about reality without getting bogged down in messy practicalities.

Let's take Spotify as an example. I often hear that artists complain that they get paid micro-cents per listen and that streaming is destroying their livelihood. I've no idea how much a recording artist gets every time their song is played on the radio, and I've no idea if Spotify is better or worse than the record deals generated by corrupt studio bosses.

So let's reduce Spotify to a toy example. Imagine a streaming service where people pay a fixed monthly subscription to get unlimited access to media.

This streaming service has only two users. They each pay £10 for the service. The service has no operating expenses and takes no profit. That money needs to be fairly split between the artists. We do not care about record companies, publishers, contracts, fees, taxes etc. We'll ignore copyright lengths as well. Some media is more expensive to produce than others, again ignored. We're assuming all things are equal.

So, what should happen in this scenario:

User 1 listens once to a 3 minute song by Ariana Grande. User 2 listens once to a 3 minute song by Billie Eilish.

That's all they do for that month.

I think most reasonable people would say that artists A & B would split the money evenly. All things being equal, they each get £10.

Now let's take a different scenario.

User 1 listens to 90 songs by Ariana Grande. User 2 listens to 10 songs by Billie Eilish.

How should the money be fairly split? 50:50? 90:10? Something else?

I asked this question on Mastodon:

What I find interesting is that there isn't an obviously fair split. Some people think the service should pay out proportional to total consumption across all users. But a significant minority think that the money should be split per individual customer. Both positions are reasonable and I can see the arguments for each.

Is it fair for some users to subsidise others? Is it fair if artist A gets paid less per stream than artist B? Should there be a maximum or minimum amount an artist can earn? Would people accept a logarithmic formula which decreases the profitability of an artist the more times they are streamed?

Mammals like us have an innate need for fairness. Our primitive monkey-brains can't exactly quantify what makes something unfair - but we know it when we see it.

When artists complain about fairness in streaming, they're probably right; it is unfair.

But when pundits start saying there is an obviously fairer solution, they're probably wrong.

And that's the purpose of this exercise. Even at the most reduced example, there isn't an obvious way to pay artists fairly.

Once you scale up to millions of users, in different countries, interacting with complex licencing regimes, exclusive deals, songs of varying lengths and of varying copyright, etc then it becomes unsolvable without radically reconfiguring how we approach consumerism.

I've written before about the Feynman Algorithm which is a universal method for solving any problem. It goes:

1. Write down the problem.
2. Think real hard.
3. Write down the solution.

I think step 0 needs to be a von Neumann reduction:

0. Reduce the problem to its very simplest use case.
1. Write down the problem.
2. Think real hard.
3. Write down the solution.
4. Return to step (0) and increase the complexity.

I suppose what I'm trying to say is if you can't handle me at my worst, you don't deserve me at my best if you can't solve a problem at its simplest level, you can't solve it at its most complex.

He makes three pretty good points.

1. Companies only pay tax on their profits.
2. Politicians shouldn't make laws with loopholes.
3. International laws need harmonisation.

I agree with his second two points - although no-one is forcing Google to exploit the loopholes that it finds - but I am not sure I agree with the first.

Fairness, so it seems, is hardwired into our brains and our societies. People naturally get very angry when they encounter unfair situations. Even monkeys react badly when they see other monkeys being treated with favouritism.

I think that's what's happening here. As an individual, I don't get to only pay tax on my profits - I have to pay income tax and National Insurance on every penny I earn.

There are, as far as I can tell, only a few exceptions. If I donate money to charity through Payroll Giving or put money in my pension - I get a small measure of tax relief. If I receive rental income, I can offset any interest on a mortgage against it. That's pretty much it.

The tens of thousands of pounds of student loans that I owed did not count against the amount of tax I paid. It cost me £3,000 to get a train to work and that severely cuts into my "profit" but doesn't count against tax. I have to live somewhere - but mortgage relief was abolished by the Labour Government in 2000. Heating, electricity, education, food - these are all legitimate expenses which I cannot offset against the amount HMRC wants to take from me.

I'm sure you can think of dozens of other examples. Expenses which a business can use to reduce their tax liability but which ordinary people cannot. And we haven't even touched on the inability of the average citizen to stuff their loot in an off-shore tax haven!

HMRC produce a great Android app which tells you roughly how the Government spends its money. It also shows you where it gets its money. Business, so it seems, pays a rather modest share by way of corporation tax. I'm sure they pay lots of other taxes and invest in other ways but guess what so do I!

I'll leave it to the armies of lawyers to figure out of Google, Amazon, Vodafone, and the like are acting correctly. But it is undeniable that a large number of people have trouble with large scale tax avoidance not because of its legality but because it is unavailable to ordinary individuals.

Fairness is really hard to codify, it's true. But when a multi-billion pound corporation gets to pay tax only on its profits, and individuals get no such relief, that feels profoundly unfair. And, like the chattering monkeys that we are, it enrages us.