What kind of risk-taker are you: Maximax, Minimin, or Minimax? A decision-making framework
Today, in our series on demystifying AI, ML, and applied algorithms, we’re looking at gains, regrets, and risks.
TL;DR:
You can wire your algorithm or your brain to make decisions based on:
- Maximizing the payoff at all cost (risk taker) — Maximax
- Maximizing the minimum payoff (risk aversion) — Maximin
- Minimizing the potential regret (loss or missing out) — Minimax
We all want to avoid regret while maximizing success in what we do. Oh, and all that with controlled risk, of course. How do we model that?
Jeff Bezos made his Regret Minimization framework pretty famous:
Now…while this is inspirational, I have a hard time applying that to most of my decisions. I am pretty analytical and I need more data to make decisions.
The regret aversion ( or anticipated regret) decision theory.
The idea is that, when facing a decision, individuals might anticipate regret and thus incorporate in their choice their desire to eliminate or reduce this possibility. Conscious anticipation of regret creates a feedback loop that elevates regret from the emotional realm — often modeled as mere human behavior — into the realm of the rational choice behavior that is modeled in decision theory.
In other words, there are ways to anticipate regret and model our decision-making process.
Anticipated and Experienced regret
Let’s consider this simple example.
You can get:
- $40 now, or
- We can toss a coin and if you guess correctly, you get $100 (otherwise, $0)
Choice A minimizes the risk but also the possibility of regret since the coin won’t be tossed (and thus the uncertainty not resolved).
If you pick B and guess wrong, this will induce regret (worth $100) but potentially have the highest gain.
People usually over-simplify this by asking the question: are you a risk-taker or are you always going for certainty?
Life is never quite as simple as choosing between A and B. We deal with nuances, a range of options, timely emotions, etc… How do we go about quantifying these emotions (risk, regret, gains) in our decision-making process?
Data-driven assistance to decision making — A simple example
To illustrate this theory, let’s take an (overly simplified) marketing example of choosing a landing page design.
We created 4 landing pages, all very different in messaging, and estimated the conversion rates for all of them with an optimistic, pessimistic and neutral outlook.
The table below shows the conversion rate for each.
The question is then which output level to choose?
Maximax
The maximax rule involves selecting the alternative that maximizes the maximum payoff available.
Looking at our payoff table, the highest maximum possible conversion rate is 12%. This happens if we choose the provocative Landing Page with a positive response.
This approach would be suitable for an optimist, or ‘risk-seeking’ investor, who seeks to achieve the best results if the best happens.
Maximin
The maximin rule involves selecting the alternative that maximizes the minimum pay-off achievable. I would look at the worst possible outcome at each supply level, then select the highest one of these. This is a guarantee to minimize my losses. In the process, I miss out on the opportunity of making big profits.
Looking at the table:
- For the futuristic Landing Page, the minimum conversion rate is 1.5%.
- For the comparison Landing Page, the minimum conversion rate is 2%.
- For the product-based Landing Page, the minimum conversion rate is 3%.
- For the provocative Landing Page, the minimum conversion rate is 0%.
The highest minimum payoff arises from the product-based landing page. This ensures that the worst possible scenario still results in a conversion rate of at least 3%
This approach would be appropriate for a pessimist who seeks to achieve the best results if the worst happens.
Minimax regret
The minimax regret strategy is the one that minimizes the maximum regret. It is useful for a risk-neutral decision-maker. Essentially, this is the technique for a ‘sore loser’ who does not wish to make the wrong decision.
‘Regret’ in this context is defined as the opportunity loss or cost of having made the wrong decision.
To compute this, we need to find the biggest conversion rate for each LP row, then subtract the actual rate.
The maximum regret for each choice are as follows:
- For the futuristic Landing Page, the maximum regret is 6.5%.
- For the comparison Landing Page, the maximum regret is 3%.
- For the product-based Landing Page, the maximum regret is 1.5%.
- For the provocative Landing Page, the maximum regret is 12%.
If we employ the minimax regret criterion, we would want to minimize that maximum regret and therefore go with the product landing page.
This is an illustration only to understand the concept. In our marketing efforts, things are never that clean-cut, nuances are everywhere and we need to take more data into account.
Moving on to a more advanced model
Suppose an investor has to choose between investing in stocks, bonds, or the money market, and the total return depends on what happens to interest rates. The following table shows some possible returns.
Returns on investment depending on interest rate
The Maximin (maximizing the minimum pay-off) choice based on returns would be to invest in the money market, ensuring a return of at least 1.
However, if interest rates fell then the regret associated with this choice would be large. This would be 11, which is the difference between the 12 which could have been received if the outcome had been known in advance and the 1 received.
The regrets table for this example, constructed by subtracting actual returns from best returns, is as follows:
Using a minimax choice based on regret, the best course would be to invest in bonds, ensuring a regret of no worse than 5.
Now, we need to compute a little more and find if permutations of these investments would yield an even lower minimax. And yes! A mixed investment portfolio would do even better: 61.1% invested in stocks, and 38.9% in the money market would produce a regret no worse than about 4.28.
How do we apply that in Marketing?
One way to think of it is: what is the reaction (conversion rate is one indicator of it) of my visitors to different content.
Why is it tricky?
Let me get to the point: we, humans, can’t create this table.
Filling the table is a result of extensive experiments (A/B testing can’t solve this problem, and that’s why it fails 80% of the time. We covered why here)
- Listing the type of messaging/content involves bias (“I feel that the types of content that might work are…”) which is ok, but prevent from testing exhaustively. We need a data-driven way to come up with content
- The “…” for the profile/sensitivity row is actually made of billions of potential values and combinations of visitors’ feature sets
- Like the investment portfolio, the winning overall content will be made of elements driving various emotions. We can picture that as a portfolio of variation of content
- This portfolio of content will vary from one visitor to the next, so we need intelligent segmentation
The solution: Machine Learning + AI
Machine Learning can process large datasets and gather results for the billions of permutations in a table that is not humanely visualizable anymore.
AI can help in generating and recommending content based on emotions, affinities, concept extraction, and summarization techniques.
The combination of both and using a regret minimization algorithm allows experimentation and optimization to run in concert.
In short: a smart marketing optimization engine learns and always minimizes regrets on deciding what content to display and what is most likely to engage and convert your visitors.
