Introduction

Evolution has designed humans to be empathetic to help others, and grateful to give back in a mutually beneficial transaction. Unfortunately, not all series of exchanges are fair long-term.

Whether these relationships are worth it is ordinarily up to intuition, but there are more accurate ways of reaching a conclusion. Not unlike Fermi guessing, this is a way of plugging multiple estimates into one equation to output an answer as to how much overall utility your company grants you.

Variables

These are the variables that will be used in the equation:

Empathy Level: How much utility one gains from the emotional satisfaction of giving.

A score of 1.0^[1] indicating you gain equal utility to that which you lose.
A score of 0.0 indicating no utility gained when spent.

$Empathy (E) = \frac{Utility gained}{Utility spent}$

Gratitude Level: How much one gives back after being given.

A score of 1.0 indicating you repay exactly the same amount of utility that they spent on you.
A score of 0.0 indicating you do not repay any utility.

$Gratitude (G) = \frac{Utility spent}{Utility gained}$

Imagine one friend is teaching another which keyboard shortcuts to use for a piece of software, or a poor friend lending money to a richer friend. In either of these situations the utility spent does not match the utility gained. The ratio of gain to loss can be summarised as the efficiency of the transaction.

$Efficiency (N) = \frac{Utility your friend gains}{Utility you spend}$

(Note that if your friend spends X utility on you, and you gain <X, gratitude uses the original X value, as your brain will likely compensate).

These values will hereafter be referred to as follows:

Metric	You	Your friend
Empathy Score	Y(E)	F(E)
Gratitude Score	Y(G)	F(G)
Efficiency	Y(N)	F(N)

While every interaction is different, over enough time there is an average, in which case every favour happens in six steps:

You spend X utility helping your friend.
You gain Y(E)*X utility.
Your friend gains Y(N)*X utility.
Your friend feels gratitude and decides to repay F(G)*X utility.
Your friend regains F(E)*F(G)*X utility.
You gain F(N)*F(G)*X utility.

The Maths

Change in Utility	You	Your friend
Utility gain (Concrete)	F(G)F(N)X	Y(N)*X
Utility gain (Empathy)	Y(E)*X	F(E)F(G)X
Utility loss	X	F(G)*X

If you put all this together you get the following:

Beneficial to you if	F(G)*F(N) + Y(E) - 1 > 0
Beneficial to your friend if	Y(N) + F(E)*F(G) - F(G) > 0

Ad...

Posts

Wikitag Contributions

Comments