# Do probability and statistics apply to the decisions of an agent with libertarian free will?

Do probability and statistics apply to libertarian free agents? Can a libertarian free agent have a statistical tendency towards certain decisions? Would it make sense to say, for example, that there is a 80% chance that a given libertarian free agent will prefer option A over option B? In other words, can the decisions of a libertarian free agent be governed by a probability distribution? Bonus question: could this probability distribution be manipulated?

• A variant on this question I've thought about: if libertarian free will is true, suppose God restores the entire state of reality back to the way it was in a previous moment (including any non-physical aspects of reality that change with time), just before agent A made a choice, and then lets time play forward again. Suppose God does this over and over, an infinite number of times. Will the ratio of diff. possible choices A makes converge to some specific fraction in the infinite limit, if so is free will modally identical to random selection from the corresponding probability distribution? Jun 21 at 15:41
• @Hypnosifl He would have to put himself back in time too. Time cannot be reversed by whatever agent wthout the agent itself being reversed too. Hence the reverse is not possible. Jun 21 at 22:07
• @Deschele Schilder - Even if one adopts a philosophy in which God changes in time in some way, couldn't God make it so that his memories of past "replays", or any other changes in his own internal "state", don't later any causal effects He has on the world, i.e. His causal "inputs" on the physical world or on souls (or other non-material reality) are the same in each replay, at least up until the point where the replays diverge due to choices by agents other than God? Jun 21 at 22:11
• @Hypnosifl He could but then he must be outside himself. So there must be two of him. Maybe because he is God he can do that, but then there have to be three of him... Jun 21 at 22:21
• @DescheleSchilder Why would refraining from acting differently imply being "outside himself"? I'm only saying God needs to act the same in terms of His causal effects on the created world, not in terms of any causal effects God's memories may have on other aspects of God's own 'internal state'--if there are aspect of that internal state that are different on each replay, but the differences have no causal effects on the created world, those differences should be irrelevant to whatever account we give of why the finite agent A made different choices on different replays. Jun 21 at 22:33

Consider the example given here: What's the "opposite" of emergence? of modelling traffic flow as a gas in pipes. No one thinks the complexity of human drivers changes. But, their freedim to act is constrained, making their actions, on average, much more predictable. Once in a while, someone may drive the wrong way down a highway, or start a road-rage incident, or be moving in a convoy, and the model won't be able to handle it.

There are many prosaic constraints on our actions, like gravity. These make us easier to predict too. But no, have no impact on libertarian free-will.

Same as my answer to the question you linked, lets consider the following situation:

• There are two options A and B
• Option A is largely preferable to B, unambiguously, and this information is available to everyone.
• For some reason, only 20% of people can use option A (supply can't match demand, access is restrained, etc)

Then it's easy to predict that roughly 20% of people will choose A.

The example is quite contrived but it illustrates how consistent trends can be observed even if people have libertarian free will: people will freely chose the best option, as long as its available or the cost for the competition to get it does not nullify its advantage.

• "people will freely chose the best option" - why the best option, why not the worst option? Aren't they free to choose the worst option? Jun 21 at 3:49
• @spiritrealminvestigator: because they are not stupid. It makes sense that they will freely chose the option they prefer if correctly informed. It's always possible to construe a choice in this fashion: the samurai chose to open his belly because he prefered death to dishonor. Had he preferred to live, he could have just fled. Etc... Jun 21 at 3:56
• Are you suggesting that their lack of stupidity determines them to choose the best available option always? Is intelligence a deterministic function? How do you reconcile that with libertarian freedom? Jun 21 at 4:04
• @spiritrealminvestigator: Sorry i should have used a more neutral formulation. People will freely choose the path they prefer, by virtue of the definition of "prefer". Even "I will choose the worst choice B to prove armand wrong" is still a reason for them to prefer B. If you think that raises lots of paradoxes, you are like me. That's the fascinating complexity of the problem of free will. Jun 21 at 5:08
• @desheleschilder: some choices come very close to unambiguous. For example people will prefer to pay less for the same product if it's in the store next door, etc... Free does not mean random, and some trends just make sense under the paradigm of free choice. That's why I don't think the OP's question is a solid argument against free will. It becomes much stronger once it can be demonstrated that people's choice can be influenced without their notice, for example with product placement in movies. Jun 21 at 23:10

A single agent cannot have any statistical tendencies in its behaviour. Large groups of agents can. Politics and marketing are especially interested in finding statistical tendencies in people's behaviour.

These tendencies can be manipulated through propaganda and advertizing. People's preferences can be changed to a statistically significant extent.

However, this does not eliminate free will. People will vote the new guy or buy the new product out of their own free will.

The main point of libertarian free will is that we can choose only our actions according to our preferences, but we can never choose those preferences.