A Decision Theorist’s Bhagavad Gita

Don’t let the action’s fruit be your motivation

Bhagavad Gītā

An act may [...] be identified with its possible consequences

Savage: The Foundations of Statistics

Abstract

We analyze and interpret the Bhagavad Gītā from the point of view of decision theory. Arjuna asks Krishna for help in his decision of whether to fight or not. Broadly speaking, Arjuna prefers consequentialist arguments, while Krishna stresses the warrior’s svadharma. In doing so, Krishna can be considered to suggest a “new” twist on the standard decision model, in line with reason-based theories of choice. We also argue that Krishna’s svadharmic point of view can fruitfully be seen as an example of the Rational Shortlist Method.

Appendices

Appendix

List of Symbols

• $x\succsim y$: (weak) preference (x is at least as good (as preferable, as virtuous, as compatible with svadharma) as y)

• $x\sim y$: indifference (x is as good as y)

• $x\succ y$: strict preference (x is better than y)

• A:  set of actions

• C:  set of consequences

• $A\times C$: set of action-consequence tuples $\left[ a,c\right]$

• $\left. \succsim _{C}\right.$: preference on C

• $\left. \succsim _{A}\right.$: preference on A

• $\left. \succsim _{A\times C}\right.$: preference on $A\times C$

• $\succsim$ on A:  preference on A derived from $\left. \succsim _{A\times C}\right.$

• $f:A\rightarrow C$: consequence function

• W:  set of states of the world

• $g:A\times W\rightarrow C:$ uncertain-consequence function

• $\max \left( A^{\prime };\succ \right)$: those actions from $A^{\prime }$ that do not have a better action in $A^{\prime }$

• ${\mathcal {P}}\left( A\right)$: set of nonempty subsets of A

• $\gamma :{\mathcal {P}}\left( A\right) \rightarrow A:$ choice function

Theorem 1

For a proof of the theorem, we assume two actions a and b where a is chosen at $A^{\prime }$ while $b\in A^{\prime }$ and $a\in A^{\prime \prime }$ hold. Then, it cannot be the case that $b\in A_{sv}$ and $a\in A_{pa}$ (because then a would have been eliminated in the first round at $A^{\prime }$ ). Three possibilities remain:

• $b\in A_{sv}$ and $a\in A_{sv}$ . Then, both a and b survive the first round and $f\left( a\right) \left. \succ _{C}\right. f\left( b\right)$ . In this case, $a\in A^{\prime \prime }$ cannot lose out against b in the second round.

• $b\in A_{pa}$ and $a\in A_{pa}$ . Then, there is no other action c in $A^{\prime }$ with $c\in A_{sv}$ (otherwise, both a and b would have been eliminated). Therefore, we have $f\left( a\right) \left. \succ _{C}\right. f\left( b\right)$ and pursue as under the first bullet.

• $b\in A_{pa}$ and $a\in A_{sv}$ . Then, b is eliminated in the first round under $A^{\prime }$ as well as under $A^{\prime \prime }$ (if b belongs to $A^{\prime \prime }$).

This concludes the proof.