Explain the ARGUMENT GAME
Ronald Loui
Ronald Loui
Ronald Loui
Published May 28, 2026
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Ah yes, the Argument Game. You need about 8 decks of small cards.

I thought this was going to be my major intellectual legacy. Then the Colvin Diagram came along (more about that later!). I thought like Lewis Carroll, that logic could be digested easily as a game. (Alice Liddell used to complain that Dodgson would host dinner parties then make everyone sit around and play his boring logic game!)

This was supposed to teach people how to reason analogically from precedent. Defeasibly. Dialectically. Analogically. To make the world a better place: a gift to society more accessible and longer lasting that the review of Prakken in JOURNAL OF SYMBOLIC LOGIC.

Well, William Chen liked playing it with me, and he wrote a book on MATHEMATICS OF POKER as a math PhD student at UCB. So, that's something.

It was designed to help us understand what would be a fair and effective division of serial search time for reaching a resource-bounded conclusion through pro and con dialectic. That's a mouthful. It was for figuring out how to program beyond the LMNOP legal reasoner we wrote in LISP in the early 90s. And it turned out to be fun!

The 9 of hearts is a proposition or claim. The 9 of diamonds is the same claim. The 9 of clubs is the negation. So is the 9 of spades. The 2 of hearts is a different "fact claim", and black 2 is its negation. Like p and not-p, q and not-q.

You deal three cards and say "this is evidence. Both parties agree on these facts of the case."

Then you deal about 20 cards face up. These are the propositions decided in prior cases that you know about. The facts of those prior cases are a stack of cards under (or adjacent to) each face-up card. You are going to argue that the evidence merits a specific claim based on similarity to the prior cases, say red Queen when the evidence for the current case/situation are showing black 3, red 10, and red Ace.

If you want to make a simple argument for a claim like red Queen, you find the evidence claims in the stack of cards where that claim was decided. So if you argue for red Queen, you find a case where red Queen was decided, and you find as many evidence claims on that case as you can; maybe you find the red 10 and the red Ace.

That would be simple. But you can chain your arguments. Suppose black 3 is an evidence card. You are trying to argue for red Queen. You don't find a black 3 among the facts of any case where red Queen was decided. But you find a black 4, and you have a case where black 4 was decided. Once you find black 3 among the facts of a black 4 case, you have a 2-step argument for red Queen: red Queen because of black 4, which you claim can be made because of black 3, which is evidence on the case for black 4.

So far so good, but each side alternates once a burden has been met, and search of cards is one card at a time. One can make a promise to ground the argument in evidence eventually, and one can challenge the promise. These have different accounting effects as search resources dwindle or are restored.

I could continue but as Steve Cousins used to say before helping Scott Hassan get to Stanford to meet Brin and Page, and write backrub which became Google, ... it seems that arguing over the rules is more fun than arguing through the cards. Perhaps.

We overlay a bidding system like that of BRIDGE to decide who wants to try to justify a claim, and with what limit on resources. There is a way to decide that one argument defeats another, hence burden is temporarily met or not. This is actually much fun because arguing defeat among arguments can itself take time. Meta-argument is not easy.

The good implementation, after three tries with Harvard summer interns (ahem, ahem), is here:

http://codereserve.us/cgi/argue7.cgi

And i probably should do a youtube demo before i die.

If you like WFF'n'PROOF (Layman was a Yalie and a real nice guy), or similar logic games, think about our argument game. If more people learned to argue in more principled ways, the world would not contain quite so many beliefs based on bad arguments. Well, that's my belief.

You don't have to be a lawyer-wannabe. But as Keynes said about probability and reasoning generally, look to the lawyers who are practical people.