Random Decisions Are Expensive

It seems obvious that it makes no sense to randomly choose between options we are presented with. In this text, I’ll set up and run a simple simulation that illustrates this. The simulation is another way to think about the impact of decision governance, even if in a very simple setting.

This text is part of the series on decision governance. Decision Governance is concerned with how to improve the quality of decisions by changing the context, process, data, and tools (including AI) used to make decisions. Understanding decision governance empowers decision makers and decision stakeholders to improve how they make decisions with others. Start with “What is Decision Governance?” and find all texts on decision governance here.

If random decisions made sense, then it would not be very valuable to know how to improve decision making, and decision governance would not be interesting at all. While it’s taken for granted that random decisions (roughly, choosing any option without a particular reason) are not the way to go in most situations where you care about the outcome, it is not easy to see just how costly they are, when contrasted with a strategy that seems simple, is not optimal, but improves on random choice.

To illustrate this, let’s say that we have two agents. They both start from the same position in a grid, and need to reach the same goal position within the same grid. To make this simple, we’ll say that they both start in the upper left corner, and their goal is to reach the lower right corner of the grid.

If an agent is in a cell of the grid, at each time period, that agent can move only to the adjacent cell in the grid. Agents, in other words, move at the same speed in the grid.

The key difference between the agents is this:

• Agent X chooses randomly the cell that they will move to next, and this agent has no memory: it moves across the grid without remembering if it already visited the cell it will visit next.
• Agent Y also has no memory, but there’s governance which tracks where Y was, compensating for lack of agent’s memory, and requires the agent to avoid revisiting a cell – every time the agent revisits a cell, they bear a cost of 1. 

X chooses randomly, and while Y has to follow a rule, it is much cheaper than X’s: Y will take fewer steps on average than X to reach the same goal from the same starting position.

For 1000 runs of the simulation of the above, X takes on average about 7387 steps to reach the goal, while Y takes an average of 2057 steps. 

Below are twenty images, each a run of X or Y. Images on the left are for Agent X, and those for Agent Y are on the right. In an image, if an agent visited the cell, then a circle is drawn in the cell, and the more times the agent visited that cell, the less transparent the color of the circle. If you download an image and zoom in, you will notice that there is a number in every circle – the number shows the number of times the agent visited that cell. Random choice on average takes longer to get the agent to its goal.

Code for simulations is available at github, here.