Friday, July 15, 2022

Dead Man Murder Problem

 

 

 

Whodunnit?

The attempted desert murders of the dead man

 

OR

 

Who's Afraid of the Trolley Dilemma?

 

This item is based on a version I read some decades ago, which was published as a puzzle for the Artificial Intelligence software community; unfortunately, I am unsure of the author of the original (Donald Michie?), but I have elaborated on the version that I then read.

As I see it this problem beats the Trolley Dilemma for genuine substance, but both of them are based on neglect of the ethical principles involved: nearly everyone who tries to resolve the matter naïvely begs fundamental questions.  Without resolution of those questions their discussions become meaningless. If you happen to be insufficiently familiar with the Trolley Problem, read the article in Wikipedia, where there is a good discussion.

At the time of writing I do not know of a published version of any discussion of what I here call the "Dead man murder problem", but anyone who can refer me to any earlier version, or to an interesting elaboration, shall be most hospitably received and acknowledged.

Alf, Billy, Charlie, and Dennis crash-landed unhurt when their aircraft failed over a desert, landing among dunes far from anywhere. 

Alf so bullied the others that they hated him and each privately decided that he couldn’t hold out for rescue while Alf lived.

Billy surreptitiously put a slow leak into Alf's water canteen.  Charlie did not know of the leak, so he dissolved some cyanide in the water. Dennis did not know of the others’ attempts, so he  dissolved some gelatine in the water while the others slept.  This solidified the water once it had cooled, so that it could not leak, but also could not be poured out, giving the impression of a vessel containing no liquid, though if it were dug out with a stick or similar rod and swallowed, it could have kept Alf alive as effectively as liquid water would have, if it had not been for the cyanide. 

Alf set out on a walk towards the river, telling the others to wait by the wreck, or he would skin them when he returned, but as soon as he had gone the other three hurriedly left in another direction, taking the rest of the water from the wreck and abandoning him to his fate.  Alf was within walking distance of the river if only he had had enough drinking water to get him so far, but not realising that there actually was salvation from thirst, if not from cyanide, in the water bottle, he died of thirst before he could reach the river, or perhaps on his way back to the plane where he thought the others would have been waiting for him. 

The other three were rescued, arrested, and charged with his murder.  In that country murder carried a mandatory sentence of death by hanging, so, not surprisingly, each pleaded not guilty of murder, though some reserved in extenuation, a plea of attempted murder, arguing that nobody had done anything that killed Alf, so that in fact there was no murder at all. 

Billy argued that his leak had done Alf no harm because it was not the leak that had  deprived him of water, and in fact he had had enough water with him at all times, and besides that his leak even would have saved him from the cyanide if it had not been for the gelatine.

Charlie showed that Alf had not died of cyanide, and as he had done nothing but administer cyanide, he could not possibly be guilty of harming Alf in any way.

Dennis argued that that the water contained in the jelly in the water bottle could have kept Alf alive till he reached the river, so that actually his action had both conserved the water that would have leaked out, and saved  Alf from dying from either thirst or cyanide —  if only Alf had elected to be saved by it. Alf had died of his own ignorance, not murder by thirst or cyanide.

And yet, Alf is dead, and would not have been dead if none of the others had tried to kill him. And for extra credit, if Alf had caught them in time, the rest of them would have been dead, so they could all claim merit for saving of innocent lives. Still, yet again, each had tried to kill him, and each one's deed would have killed him if the others' deeds had not interfered. But no individual one had succeeded more than any other; no one had done any one thing that had harmed Alf. And what about the plea that the actions of some of them had saved Alf’s life, if not for long, of course?

And they had neither colluded nor conspired. . .

 

Well, ultimately, who was guilty of what, if anything? Alf of suicide, or any of the others of anything?

 

6 comments:

  1. This comment has been removed by the author.

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    1. Nice try, but there are difficulties: poison in stomach did NOT happen, so POISON could not be responsible. Accordingly you can't hang Bert.

      Either of the other two was a lifesaver rather than a murderer, because they prevented the poison from killing the drinker even faster than thirst could. How can you hang someone for lifesaving? The water was not removed, so they could hardly be accused of killing Alf by thirst.
      And, with apologies for not mentioning it, in that country the sentence for murder is hanging; I'll edit the article to clarify that. But either way, how many eighths of a hanging is the appropriate sentence for one third of a murder? And how does one give three eighths of a life sentence? Sent\ence him to eight days in prison, keep him in jail for three days, hang him, then keep his remains before disposing of them five days later?

      Hospitable certainly, but a bit unsatisfying in some ways, I reckon.

      The jelly meant that the water had NOT been removed, so how could Charlie or Dennis be guilty of killing Alf of THIRST?

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  2. If sabotaged and spiked water not in sabotaged canteen and not in stomach then canteen saboteur not guilty of canteen sabotage and spiker not guilty of water spikery and water saboteur not guilty of water sabotage else if in canteen and not in stomach then three-eighths of a life sentence for canteen saboteur and one-quarter for spiker and three-eighths for water saboteur else if not in canteen and in stomach then one-quarter for canteen saboteur and one-half for spiker and one-quarter for water saboteur.

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  4. If charged with murder and attempted murder and arraigned then
      if pleaded guilty to murder then
        three-quarters of a lifetime in prison
      else
        if tried by a jury of ten or so then
          if pleaded guilty to attempted murder then
            if found guilty by majority of murder then
               a lifetime in prison
            else
               quarter of a lifetime in prison
          else
             if found guilty of murder then
               death by hanging
             else 
                if found guilty of attempted murder then
                  half a lifetime in prison.

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  5. It's been a while since I came across this example, and it seems to have grown over time (Dennis is a new wrinkle). I used to think the version I knew (without Dennis) was clear-cut, but on re-thinking it decades later I realized I had simply been wrong.

    I now think it is helpful to simplify the problem. We can just let Billy and Charlie shoot Alf in the head (simultaneously), and have both argue that Alf would still be dead without their action. I think even this simple version captures the essence of the problem: we have a logical OR function with two inputs equal to 1, jointly causing the output to be equal to 1, with the property that inverting either input leaves the output unchanged but inverting both inputs will change the output. We have no problem understanding such systems mathematically, but the issue is that the language of causality simply does not extend to situations with multiple causes, which frankly is an embarrassment both for natural languages and for e.g. judicial systems that rely heavily on natural languages (I'd be interested to know if there is a natural language with a more sophisticated treatment of this).

    I'd recommend "Causality" by Judea Pearl as the most sophisticated approach to putting causality on a solid philosophical and mathematical footing (that I've come across), but I think it doesn't actually address this problem at all (and would end up acquitting all parties). So if, say, we have an intuition that the right solution would be to somehow divide up the guilt between the parties, and we want a theory that would justify such an intuition, then even our best (?) mathematical description of causality is still in its infancy.

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