AI & Law: Chess-like State-Space complexity

mediumThis post was originally published by Lance Eliot at Medium [AI]

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Practice of law as viewed via chess playing and AI

by Dr. Lance B. Eliot

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Key briefing points about this article:

  • Some liken the practice of law to the playing of chess
  • Lawyers need to conceive of their legal moves and countermoves related to opposing counsel
  • AI chess-playing systems have gotten quite good and there are lessons to be learned therein
  • It is handy to consider the state-space complexity in the construct of legal argumentation
  • Predictions are that the use of AI legal reasoning will ultimately be integral to legal arguments

Introduction

The odds are pretty high that you know the name Bobby Fischer, considered one of the greatest chess players ever.

Anyone with small children that play chess is apt to have told their offspring that someday they might be as good at chess as Bobby was. It seems that every time a youngster even appears to play chess well, adults begin to refer to the child as yet another Bobby Fischer.

In the entertaining and informative movie Searching for Bobby Fischer, there is a refrain repeated several times, consisting of the stern admonishment to the chess-playing child prodigy in the story: “Don’t move until you see it.” This might seem like an obvious piece of advice, namely, to think before you act, but the rub is that these chess matches are a nail-biting timeboxed event and for each moment of not taking your turn the clock is winding down. Seconds and ostensibly split seconds can end-up being the difference between winning and losing a timed chess match. In that sense, if you are thinking during your turn, when you are on the clock, as it were, you’d better think fast.

The problem with thinking fast is that it can inextricably equate with not thinking completely or otherwise shortcutting the thinking process.

Therein lays the conundrum. If you are willing to undercut your thinking time, you’ll save those precious seconds, perhaps needing them later on. But this also leads to the possibility that you are making a somewhat rash move that was not especially thoughtful, perhaps a dreadful move that will ultimately put you into a losing checkmate, and ergo having saved time was counterproductive in the end.

One advantage for lawyers and the act of lawyering is that you are seldom on the clock, at least not in the same manner as a traditional chess match (as an aside, chess is classified as a two-player zero-sum “perfect information” game that has no hidden info about the gameplay per se, i.e., all actual moves are seen by both players).

Sure, when standing before the judge and arguing your case, there is a devout semblance of time being of the essence. If you are asked a question and cannot reply with a rapid and sensible response, it makes you seem ill-prepared and also implies that your loss for words arises because your case is decidedly weak and there isn’t any suitably defensible reply to be had. Those moments of tension and time-based stress are as real as those when sitting at a chessboard and having to ascertain what move is best to make.

Shifting gears, let’s consider what happens during chess playing and leverage what we know from the application of AI to chess-playing to see if the same fundamentals can be applied to the act of lawyering.

Indeed, there are predictions that we will ultimately have AI applied to the law and the practice of law that is capable of directly assisting human lawyers, including eventually reaching truly autonomous AI legal reasoning. In the case of autonomous legal reasoning, it is presumed that this kind of AI could potentially take on the role of a lawyer, a judge, and other legal professionals, operating without the need for any human assistance.

For details on this and other AI and law topics, see my book entitled “AI and Legal Reasoning Essentials” at this link here: https://www.amazon.com/Legal-Reasoning-Essentials-Artificial-Intelligence/dp/1734601655

AI, Chess, and the Practice of Law

With that preamble, let’s unpack the AI chess playing insights.

When playing a game like chess, each move is referred to as a ply. I make a move, and then you make a countermove, which means we are now two-ply into the match. When I made my original move, hopefully, I was anticipating the possible countermoves that you would make. I don’t know for sure what move you will opt to do, though I can possibly make mental guesses.

For example, I can guess that you won’t make a move that seems entirely like an outright blunder. Unless you’ve never played chess before, you are likely to realize that you need to protect your king, and thus if you immediately make a move that puts your king at risk, this will seem foolhardy and I would not anticipate your doing so. Of course, it could be a trick, lulling me into believing that you are doing something amiss, and possibly seeking to catch me off-guard accordingly.

If you have not yet thought about the number of moves and countermoves that can occur in a game of chess, it is a really large number.

This is worth mentioning because some people wonder why you don’t just imagine in your mind all of the possible moves, and then you would be ready for any move that your opponent makes. In theory, you could play, in your mind, all possible games of chess, and when you are in the midst of chess competition, you can already have a map that shows what might happen next, along with ascertaining which move you should make to in the long run reach a win.

The state-space complexity or number of possibilities is enormous. A famous mathematician named Claude Shannon in 1950 proposed that it is something like 10 to the 120th power in size (referred to today as the Shannon number). The estimated number of stars in the known and observable universe is around 10 to the 23rd power, thus many magnitudes less than the number of chess move combinations. The number of atoms in the universe is estimated at 10 the 82nd power, which is, astoundingly, many magnitudes less than the chess state-space.

The good news for lawyers is that you seldom are going to have a legal case that has the same enormity of potential moves or state-space (though it might seem like it!).

Nonetheless, just as in chess, it is important to consider your move, the likely countermoves, and your best choice for countering the countermoves, and so on.

This is why the use of AI in the law is being seen as a potential boon for preparing legal arguments. A human lawyer might not be willing or able to envision the multitude of potential moves and countermoves, while an AI-based legal reasoning system could potentially do so with ease. This could aid lawyers in thinking through their case, along with averting the potential oopsie or having failed to consider a legal argument that their opponent suddenly brandishes and catches one legally by surprise.

Conclusion

The next time you are before the bench and find yourself at a loss for words because you had not considered a suddenly introduced legal argument, you might find yourself relishing the day that your handy dandy AI-based legal reasoning system will be at your side and able to proffer the best chess-like move to win the legal case at hand.

For the latest trends about AI & Law, visit our website www.ai-law.legal

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This post was originally published by Lance Eliot at Medium [AI]

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