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Hands UP II

Today the ordinary consistory begins. And not by coincidence, we likewise finish up our base case scenario of our Consistory Game, a “prisoners’ dilemma” form of Game Theory. In the Consistory Game, our expressed aim has been to define a prisoners dilemma scenario, and analyze the situation that could arise regarding the “Team Bergoglio” scandal (for the Chronology see here) and play itself out at the ordinary consistory of cardinals that will be held on the 12th and 13th of February, i.e. today and tomorrow.

What we will present below is the payout matrix for the 4 different combinations of decisions that our two prisoners can make. We will also provide an optimal course of action that a rational prisoner, working within the constraints of the definition of this game, would take, irrespective of the decision of the other players (i.e. likewise other Team Bergoglio players). For each of the four possible outcomes, we assign a certain payoff for each prisoner that is meant to be illustrative, but captures the essence of the different moral/canonical considerations of the two parties.  Furthermore, we will define the individual decision that can be taken to reflect the optimum course of action that each player can take along with the risks associated with each decision and each course of action.

Below are the assumptions that we have established so far:

Assumption 1.
As the payoffs in the table implies, both prisoners would fare better if they choose to do the right thing. In the case of Napier doing the right thing, i.e. “confessing to promising a vote”, the cardinal would obtain a value of +5, while in the case of Francis, also does the right thing, i.e. admitting that he agreed for “Team Bergoglio” to canvass for him would also give him a value of +5. The decision to “do the right thing”, irrespective of the other prisoners’ decision will provide each with the optimal payout.

Assumption 2.
If the above is a correct assumption, then the punishment (cost) for committing a mortal sin by not admitting would be at least -5.

Proof
Because in the event of committing a mortal sin, the associated cost (punishment) can never be a lower value than the maximum benefit that the prisoner can obtain by committing that sinful act. (Cost > Benefit)

Given the above, in the table below, the Deus Ex Machina blog presents a matrix for our highly abstract yet illustrative form of the game that the bishop of Rome, Francis and Cardinal Napier can be playing at the ordinary consistory that begins today:

Table 2

According to the above payout matrix, the following are the four combinations of decisions that out players, Francis (alternatives in rows and represented by first figure) and Napier (alternatives in columns and represented by second figure) can take:

1. ADMIT/CONFESS – (5,5²)
In our Consistory Game, we already established this scenario as the optimal outcome since irrespective of what the other party does, the prisoner making the decision will receive mercy from the just cardinals, not lose their positions of prestige and power (+5) and not incur a penalty (cost) for committing a mortal sin (0). (see here)

2.DENY/ NOT CONFESS – (0,0¹)
In this scenario, we established in the previous post (see here) that the matter will not be investigated at the consistory and if any of the other cardinals raise the issue, the prisoners will deny/not confess. They will keep their positions of power and privilege (+5), but incur a cost for the mortal sin they committed by violating UDG 81 (-5).

3. DENY (Francis)/CONFESS – (-2,2³)
In this scenario, Francis denies that he asked “Team Bergoglio” members to canvass for votes. Francis incurs a cost (-5) for the mortal sin committed against UDG 81. Since Napier confessed the Ivereigh allegations are confirmed, therefore Francis is weakened in his position of privilege and power. Instead of +5 as per optimal outcome, Francis now has a value of +3. His result is (-5+3) = -2

Napier confesses, therefore does not incur cost (0), but since he dropped the dime on Francis, Francis can will retaliate, therefore Napier’s power and privilege is lowered to a value of +2. Napier’s result under this scenario is (0+2) = 2

4. ADMIT/NOT CONFESS – (2,-2)
In this scenario, Francis admits that he asked “Team Bergoglio” members to canvass for votes. Francis incurs no cost (0) since he is absolved of the mortal sin. Since Francis admitted his guilt, the Ivereigh allegation is confirmed, therefore Francis is weakened. Instead of 5 as per optimal outcome, Francis does not get (3) like in the “Deny” scenario, but a lower value of 2. The reason he is penalized for Admitting (2) as opposed to Denying (3) is due to the fact that the uncertainty as to his guilt is removed in the former case. But this marginal penalty ( 2 vs 3) is more than made up for in the fact that he avoids the mortal sin cost. Therefore, his result is (0+2) = 2

Napier does not confess, therefore incurs a cost of -5. Francis can retaliate since he got stuck with admitting to the canvassing, so he reduces Napier’s power and privilege to 3. By the same logic as in the above paragraph, the value of retaining the power and prestige by Napier has to be greater than 2 since Francis is not absolutely sure whether Napier actually did promise his vote. (He could have been one of the African cardinals that “Team Bergoglio” did not approach.) Therefore if Napier confessing lowers his power and privilege to 2, the uncertainty works in Napier’s favor under this scenario and he ends up with 3. Therefore, Napier’s final score is (-5 +3) =-2

Summa Summarum

What we can conclude from the payout matrix is the following:

1. Francis is faced with a binary decision (an either/or decision). He can either admit or deny his complicity.

If he chooses to ADMIT to his complicity, Francis will obtain a payout of either 5 (if Napier confesses) or 2 (if Napier does not confess). Both of these results are positive.

If he chooses to DENY  his complicity, Francis will obtain a payout of either -2 (if Napier confesses) or 0 (if Napier does not confess). In this scenario, Francis has only a 50/50 chance of obtaining a positive result. Furthermore, Francis is dependent on the decision of Napier to obtain a positive result.

The above description, ceteris paribus would appear to be counter-intuitive on the surface. But if one thinks it through, it is quite logical.

If he chooses to CONFESS, Napier will obtain a payout of either 5 (if Francis admits) or 2 (if Francis denies). Both of these results are positive.

If he chooses to NOT CONFESS, Napier will obtain a payout of either -2 (if Francis admits) or 0 (if Francis denies). In this scenario, Napier has a 50/50 shot of obtaining a positive result. Furthermore, Napier is dependent on the decision of Francis to obtain a positive result.

Concluding, from the above, we can infer that both prisoners would obtain the optimal payout outcome if both Cardinal Napier and the bishop of Rome Francis confessed to their complicity in the “Team Begoglio” scandal.

Not only does the payout matrix of the Consistory Game bear this out, but so does the underlying logic.

Furthermore, the above results are likewise intuitive, if for no other reason than this: they are consistent with the old Catholic maxim of “honesty being the best policy”. Actually, the above defined Consistory Game is in fact an objective proof of this very notion.

Even for Argentinians. (see here and here)

In the alternative scenarios, if either or both of the parties decided to tempt fate, they each stand a 50/50 change of obtaining a negative result. A negative result would mean that they are worse off than they were before the game began. Furthermore, it is worth pointing out that if the prisoners decide to tempt fate, their respective fates will lie in the decisions of the other prisoner. But what is worse, if the other prisoner decides to act rationally (in his best interest), the worst possible result is obtained by the prisoner who is rolling the dice. Therefore, it would not be rational for either of these prisoners to tempt fate.

Or to put it another way. When going through all the different scenarios, it becomes apparent that it would be reasonable to expect that both Francis and Napier to come forward of their own free will and resolve this issue, i.e. confess. This inference is supported by the fact that the lowest outcome for confessing/admitting is 2 while the highest outcome for rolling the dice, not confessing and relying on the other party to make an irrational decision is 0.

Think about this one for a minute or two.

I will finish off here for today.

Please consider the above as our base case scenario of the Consistory Game.

Tomorrow the ordinary consistory starts. This blog will be following the information flow in order to assess how far form our Consistory Game the actual results varied. We will also be using this defined prisoners’ dilemma to assess the information flow and interpret the decisions that were made. That is if any were made.

So stay tuned and DON’T TURN THAT BAT DIAL!