Tuesday 13 March 2012

Belief Theorem, March 12, 2012

Why it is rational to believe in a Creator: A simplied analytical framework

Overall Utility, U = UE + UH
UE is utility in life on earth
UH is Utility in the life hereafter if there is one

Utility in life on earth

It is possible that a human agent derives utility from consumption goods A [Code Permissible] and B [Sin Goods]. There is, however, a physically limited maximum consumption (due to finite lifetime) of these on earth. Utility is increasing in A and B and there is no saturation point.

Say, effort is misery and leads to disutility. Believing takes effort and consumption of A and B does not require effort.

To make it easy, if an agent does not believe, enjoys maximum earthly consumptions of A and B, and derives maximum earthly utility of UMax,E. An agent who believes in Divinity System and also does not consume B (sin goods) on earth, would have the lowest utility on earth, UMin,E due to no consumption of utility enhancing good B as well as maximum earthly misery/disutility from maximum effort toward belief. Someone believing but not practicing as well and not putting as much effort toward belief, would have earthly utility UMid,E, with UMin,E < UMid,E < UMax,E . 

Magnitude of earthly utility UE is known ex ante once the belief and effort decisions are made.

Utility in life hereafter if there is one

Utility in life hereafter is random ex ante. States realize ex-post and state contingent utilities follow.

There are just two states: State 1: Divinity System (Creator, Code, Reward /Penalty in life hereafter) exists, ex ante probability p; State 2: No Divinity System, ex ante probability 1-p.

If State 1 realizes ex post
i. Agent believed in Divinity and Lived with Maximum Piousness (no consumption of sin goods)
          An infinite time in heaven with unlimited consumption of A and B
          Utility in Hereafter = UMax,H
ii. Agent believed in Divinity but consumed some sin goods
 A limited time in hell with limited misery, related to consumption of B on earth.
An infinite time in heaven with unlimited consumption of A and B
                   Utility in Hereafter = UMid,H
iii. Agent did not believe in Divinity
                   An infinite time in hell meaning unlimited misery
                             Utility in Hereafter = UMin,H
If State 2 realizes ex post
For all agents, utility is 0.0, as there is no life hereafter.
Expected Total Utility [with risk neutrality]

i. Agent believe in Divinity with maximum Piousness: UMin,E + p  UMax,H
ii. Agent believe in Divinity with low Piousness: UMid,E + p  UMid,H
iii. Agent did not believe in Divinity: UMax,E + p  UMin,H

Belief Theorem
Belief dominates if  UMid,H is sufficiently large, that is, p  UMid,H > [UMax,E  ─ UMid,E + p  UMin,H ], or equivalently,
p > [UMax,E  ─ UMid,E ] / [UMid,H  ─ UMin,H ]

Comment: By most belief systems (Divine Codes), the reward in life hereafter for just believing and not practicing Divine Code is clearly larger than the infinite misery from not believing (UMin,H = ─Infinity). As such, for any p>0, belief dominates.  


  1. I have benefitted enormously from ongoing dialogue with my DU Econ Bacth of 1976 gogle group friends. On analytics, thanks are due to my friend L (SZ). --MC, March 13, 2012

  2. I should have added that I am solely responsible for the opinions and errors/follies therein.

    -- MC, March 13, 2012

  3. Too bad I am late about the idea by 300+ years. I came to know yesterday (from Rabib)about Pascals' Wager.

    Pascal's Wager is an argument in apologetic philosophy which was devised by the seventeenth-century French philosopher, mathematician, and physicist, Blaise Pascal. It posits that humans all bet with their lives either that God exists or does not exist. Given the possibility that God actually does exist and assuming the infinite gain or loss associated with belief in God or with unbelief, a rational person should live as though God exists and seek to believe in God. If God does not actually exist, such a person will have only a finite loss (some pleasures, luxury, etc.). ..