Chance plurality may not be an aggravating problem for scientists, however, it raises an issue for subscribers to OC. Since the crucial formula CF employs objective chances, it might happen that it is not well-defined: depending on which level of description is used, different acts may be right, that is, different oughts might be ascribed to the agent.
To continue the above example involving dice, suppose that John, a gambler, formerly on a losing streak, has honestly decided in the morning to give all his winnings from that day to charity. For ease of exposition assume that he plays exclusively at a certain casino and only takes part in a single game of dice, in which snake-eyes doubles the player’s profit, any other outcome means that the casino takes all, the player can quit after any throw, and the casino can decide before any throw other than the first that it will be the last one. To his amazement the machine referred to above—working correctly, as certified by legitimate experts—has thrown snake-eyes a few times in a row, amassing a sizable sum of money for charity. The machine is set, waiting only for a push of the button. The casino decides the next throw will be the last one, if John decides to take it. Having integrated, in the true consequentialist spirit, any deliberations regarding risk, the non-linear value of money and so on into the value function, assume there are three outcomes:
\(O_1\), where the charity receives the money John has earned so far; assume \(V(O_1)=1\);
\(O_2\), where the charity receives twice the money John has earned so far; assume \(V(O_2)=1.5\);Footnote 7
\(O_3\), where the charity receives nothing;
\(A_1\), where John takes the throw (pushes the button);
\(A_2\), where John declines and the game ends;
and two chance functions:
\(ch_m\), the micro-level, deterministic chance,Footnote 8 according to which the chance of one outcome of the throw is 1 and the chance of any other outcome is 0;
\(ch_M\), the macro-level chance, according to which the chance of any outcome of a throw of a fair die is 1 in 6.
Assume that the distribution of microphysical properties in the gambling system is such that, in fact, if the button is pressed, snake-eyes will be thrown: \(ch_m(O_2| A_1)=1\). The act \(A_2\) implies the occurrence of the outcome \(O_1\); therefore, since chances are probability functions, regardless of which level of description is used, the expected moral utility of act \(A_2\) is 1. However, regarding the act \(A_1\) the situation is slightly nontrivial. This is because:
\(ch_m(O_1| A_1)=ch_m(O_3| A_1)=0\), while \(ch_m(O_2| A_1)=1\);
\(ch_M(O_1| A_1)=0\), \(ch_M(O_2| A_1)=1/36\), and \(ch_M(O_3| A_1)=35/36\).
It is a matter of trivial calculation that the CF assigns the act \(A_1\) higher expected moral utility than the act \(A_2\) if \(ch_m\) is used in the calculation and the act \(A_2\) is assigned higher utility than \(A_1\) if \(ch_M\) is used. In other words, one thing is the right thing to do for the agent if OC uses the micro-level chance, and another thing is the right thing to do if the macro-level chance is used. In still other words, the agent ought to do one thing under OC using the micro-level chance, and ought to do another under OC using the macro-level chance: before some choice is made regarding this matter, OC prescribes the agent conflicting obligations (or no obligation at all, if we take the CF not to be defined).
The importance of such problems for the prospects of OC depends on how often chance plurality is displayed in situations involving ethical evaluation. If you believe that it is a phenomenon only occurring in rigorously controlled and precisely described physical environments, you will probably not be moved by the fact that on such occasions it makes OC contradictory or silent. However, if you take chance plurality, at least chance duality, to be a common occurrence, for example because in most if not all examples you can think of the distinction between the macro- and microlevels is intuitively clear, then you should believe that the issue of chance plurality is of serious concern to anyone subscribing to OC—just like the reference class problem is of critical import for anyone employing probability in legal reasoning. Depending on whether chance plurality is common or not, or if it is indeed ubiquitous, some solutions we will discuss will also look more or less reasonable.
I suggest that most chancy situations are describable on at least two levels involving laws of chance. Therefore, I give high credence to the following statement: in many situations in which an agent chooses between acts at least one of which is compatible with more than one outcome, and which outcome is eventually realised depends at least partially on chance, chance plurality is exhibited. Whether this leads to frequent problems for OC depends on how often chances meaningfully differ between the various levels; however, I give high credence to the statement that if the fundamental laws are deterministic, and higher-level laws are not, problems for OC similar to the one just described indeed arise. What can we do about this?
Digression: examples involving micro- and macro-level indeterminism
The Reader will have noticed that all examples of chance-plurality mentioned so far involved fundamental determinism; this is also the case with the example about John.Footnote 9 This is not a coincidence—the still relatively sparse literature on level-relative chances contains few, if any, worked out real-life examples of nondegenerate chance on both the lower and the higher level. The prevailing opinion is that nothing stands a priori against such an option. Establishing that a situation displays two non-degenerate chances would require (at least) an argument that on both levels the six principles proposed by Schaffer are satisfied, which is bound to be a nontrivial task. I would not like for such examples to play the biggest role in my argument against the OC, since I would risk that even those otherwise sympathetic to the chance plurality idea would find them wanting. Still, not to give an impression that chance plurality as posing difficulties for the OC requires fundamental determinism,Footnote 10 I propose the following sketches of two examples which make no similar assumption.
The first case starts with the following example from List and Pivato (2015, p. 141): suppose ‘the police in a big city wish to forecast crime rates in various neighborhoods, in order to organize effective patrols. (...) The police will have to treat patterns of crime as involving non-degenerate objective chance. The chance of various crimes happening will differ from neighborhood to neighborhood: there is a higher chance of petty theft and pickpocketing at the railway station than on a quiet residential street’. Note that this is supposed to hold ’whether or not there is some physical or neuropsychological level at which each individual crime is predetermined’. Choose, then, some appropriate neuropsychological level and assume that the individual crimes are not predetermined on it, but subscribe to some chancy laws. Suppose that, on some day, in view of the recent crime-rate increase in the railway station area the officer in charge of patrol assignment can choose to allocate more officers to that region—or to send additional officers to a hitherto peaceful residential block. Suppose the neighbourhood-level objective chance List and Pivato write about indeed assigns a higher chance of crime-related incidents to the railway station area. On the other hand, the particular configuration of the city’s residents’ locations and their conditions combined with their chancy laws of individual crime-related behavior leads, on that particular day, the lower-level chance of criminal incidents to be higher in the residential block in question. It is easy to see how this leads to a case similar to the one above, involving John, the gambler.
The second idea follows a suggestion of one Reviewer who in the context of the plurality of chances mentioned currency exchange rates. My example will involve covered interest arbitrage (Levinson 2006, p. 25). The individuals under discussion live in the US; the choice to be made is whether to buy American, French or British 1 year bonds. Assume that Steven has been successful in his ForEx trading endeavours; in fact, he has amassed a small fortune and has become quite smug about his financial predictive skills. This has infuriated his aunt Jemima, firm in her belief that such proceedings are a modern form of common thievery, to no end. It so happens that aunt Jemima dies, making Steven the sole executor of her will. Its terms—by means of which Jemima wishes to teach Steven a lesson—state that, regarding a sizable sum of money left by the aunt, on the noon of the day after the will is opened Steven is supposed to announce his decision whether to invest the whole sum in American, French or British 1-year bonds, while the investment is to be carried out after exactly 7 days.
The financial situation on the day Steven is supposed to make his announcement is as follows: the interest rates in the three countries together with the spot and future exchange rates dictate that investing in American bonds is clearly the least profitable option, while British bonds are slightly preferable profit-wise to the French ones. However, since people will be selling dollars for pounds and Euros, the spot dollar/pound and dollar/Euro rates will decrease, while the 1-year forward rate rate will increase. We can consider the micro-level of description of the financial market, involving individual buyers and sellers, and the macro-level, involving larger groups and bodies, on which the Market Forces operate. On the assumption that both of these levels involve chances, we can consider the situation in which:
due to the Market Forces in operation (government decisions, bank policies etc.) the macro-chance of the British bonds ending up as the most profitable option in a week is higher than the chance that one of the two other options ends up as the most profitable;
however, due to the particular configuration of individual buyers and sellers, it is the micro-chance of the French bonds ending up as the most profitable which is the highest among the three options.
It is hopefully easy to see how one can on that basis construct an example similar to the one from the last section.
As already mentioned, I would not like these examples to be the main illustration of my argument against the OC. My objective in this paper is not to push forward the research on chance plurality; establishing whether the two examples from this subsection really ‘work’ would require e.g. a careful examination of whether we can legitimately speak about probabilistic laws in the context of economics and neuropsychological basis of human behavior—tasks which are clearly outside the scope of the current paper. I suggest, therefore, that the Reader keep in his or her mind the example of John the gambler as the main illustration of my point.