Because he withdrew before any of the dice were cast, he should have been allowed to do so, but not then allowed to eat the loser.
The remaining team members have to work and live together after they eat Whetmore, and not letting Whetmore withdraw even when his life is at stake sets a precedent that will tend to cause the members to allocate more personal resources towards the zero-sum game of getting and holding power and decision-making ability in the team.
Note that electing a leader and giving him the power to make life-or-death decisions does not suffer from the same problem. (That, by the way, is an illustration of Mecius Moldbug's general observation that formal power is often superior in its effects to informal sources of power like vague personal obligations and the power to persuade.)
Of course there might be other processes that work even better than electing a leader, but having a leader seems to work well for life-or-death decisions and for situations in which there is no time for debate.
I see it as a case of "emergency micro-government", and not taking part of the voting doesn't mean you're exempt from the laws - that would be like not paying your taxes because you voted for the party that wants to lower them, which lost the election.
i.e. the group should have one way of taking decisions that can apply to the whole group.
However that doesn't mean the decision can't be morally wrong - if the decision to sacrifice one did indeed increase everybody's expected chances of survival, then it was right, but maybe Whetmore's change of mind was right - maybe waiting one week did have a high enough chance of saving everybody. I think that aspect weights more than Whetmore's change of mind.
It depends, I think, on how you view "agreements" of that sort.
One view is that such an agreement is a contract, and in this case the contract apparently did not contain a clause covering opting out. Absent such a clause, unilateral withdrawal does give the others ground for their "breach of faith" argument.
A different view is that what was agreed on was a plan, not a contract. That's a substantially different frame: a plan is a collective course of action in the pursuit of a goal. "Breach of faith" has no place in goal-seeking behaviour; someone objecting to the plan either has a sound case or doesn't.
Breach of faith or not, Whetmore's actions strike me as not entirely well-thought-out. He would have been in a better position had he declared: "Wait, we haven't covered all bases yet; how should we handle the case when one of us is tempted to opt out?" Presenting the case as hypothetical and preserving the symmetry of the situation would have been tactically much better, under both the plan and the contract views. Under the plan view he could have ensured a dispassionate hearing for his proposed alternate course of action; under the contract view he could have pushed for fixing an oversight in the original formulation.
(N.B. I haven't RTFA, just the summary.)
There's an implicit benefit of the arrangement, which is the group not descending into anarchic conflict. Whetmore can't help but benefit from this unless he leaves the group entirely.
I think it'd be interesting to know how different people model the situation. The most obvious option for me is to view it as a form of micro-governance. Randomised cannibalism of one's peers seems almost ridiculously civilised.
The utilitarian solution, as well as a bunch of others, are discussed in Peter Suber's The Case Of The Speluncean Explorers: Nine New Opinions, which is very much worth reading.
Putting aside whether it would have been right, the four were quite probably lying about the throw going against Whetmore.
That actually makes very little sense in the context of the story. If they would lie about that, why not just say that Whetmore got hit on the head with a rock during the landslide and unfortunately didn't survive? Who would contradict them?
This is only a problem if you're a Deontologist.
From a Utilitarian perspective, they would have died if they didn't kill him. They could have killed anyone else, but that would have been the same, not better. Anything about permission or arrangements is irrelevant.
Let's add a wrinkle to the story and imagine that Whetmore tried to run away, but the others hunted him down. How strong is your utilitarian intuition in this case? If you were among the remaining survivors, would you be chanting "kill him" too?
How would that change anything? Running wouldn't make his life more valuable. It definitely wouldn't change how he feels if he dies.
Utilitarianism as most people practice it is not strictly about how many people live or die. Killing someone "fairly" and according to a predetermined set of rules presumably seemed better to the survivors than killing, say, whoever was least able to defend themselves, and worse to the survivors than eating someone who had died of natural causes, even though in all three cases the total number of survivors was the same.
I would certainly prefer the outcome (1 person dies, everyone else feels really bad about it) to the outcome (2 people die, everyone else doesn't feel bad). I think most people would in this experiment, with a small group of survivors. But there exists a number of people involved (I'll say it's smaller than 3^^^3) so that I would prefer outcome A to outcome B.
Therefore, considerations beside death could theoretically be significant, and utilitarianism can't be simplified to body count.
A fictional legal case about a team of explorers who got trapped in a cave and ate one of their own to survive. Summary:
From the testimony of the defendants, which was accepted by the jury, it appears that it was Whetmore who first proposed that they might find the nutriment without which survival was impossible in the flesh of one of their own number. It was also Whetmore who first proposed the use of some method of casting lots, calling the attention of the defendants to a pair of dice he happened to have with him. The defendants were at first reluctant to adopt so desperate a procedure, but after the conversations by wireless related above, they finally agreed on the plan proposed by Whetmore. After much discussion of the mathematical problems involved, agreement was finally reached on a method of determining the issue by the use of the dice.
Before the dice were cast, however, Whetmore declared that he withdrew from the arrangement, as he had decided on reflection to wait for another week before embracing an expedient so frightful and odious. The others charged him with a breach of faith and proceeded to cast the dice. When it came Whetmore's turn, the dice were cast for him by one of the defendants, and he was asked to declare any objections he might have to the fairness of the throw. He stated that he had no such objections. The throw went against him, and he was then put to death and eaten by his companions.
Was it right for them to kill and eat someone who wanted to opt out of the arrangement?