Decision rules

If you were wondering how predicted ratings (utilities) are turned into share predictions in the simulator, decision rules (sometimes called choice rules) are how this is done. They can be thought of as a second layer in conjoint analysis models - translating the predicted ratings (utilities) into either choices or probabilities of choice for the scenario you selected on the control tab. They are calculated at the individual level.

Which decision rule should you use? Whichever does the best job of predicting actual market shares, otherwise you can use theory to guide you (explained more below).

REMEMBER: if you change decision rules and you had calibration already switched on prior to this, you need to rerun calibration using the new rule; by switching calibration off and then on again.

Introduced by Professor Paul Green, the father of conjoint analysis. Maximum utility translates the predicted ratings (i.e. total utillities) for each product in a scenario into a choice - it does this at the individual survey participant level. It follows the simple principle of the largest utility wins being awarded a count of 1 per individual (unless weights are applied), while ties are split using the simple formula 1/ties. In theory, it is most suited to durable product markets, or any infrequently purchased product or service that will likely be only purchased once within your survey’s forecast horizon (e.g. next 12 months). Examples might include appliances, cars, choice of bank or schools. That said, it can sometimes also do well with more frequently purchased items. It is also used for ‘product line’ scenarios.

An advantage of maximum utility over probabilistic rules such as BTL or MNL (used in Choice Based Conjoint), is that it does not make the IIA assumption. This means it does not inflate shares of similar / identical products like BTL would.

Bradley Terry Luce (BTL) was also introduced into conjoint analysis by Green; although he didn’t invent it, it was borrowed from other types of marketing research models.

The probability of purchase is calculated by dividing the utility (i.e. the predicted rating for the product) by the sum of the utilities for all products in the simulation. As mentioned, it makes the IIA assumption, and  so it is suggested that you avoid entering identical or near identical products in your simulations. Otherwise consider BTL ds.

In theory BTL is meant for markets with frequent repeat purchase.

BTL ds was added to Metrisim in July 2025. The ds stands for differential substitutability. It adjusts utilities for product similarity, the idea being that the more similar, the more substitutable and therefore more likely to cannibalize. Therefore this does away with the IIA assumption, which led to share inflation for identical or near identical products. Metrisim's algorithm was inspired by research conducted by Tsafarakis, S., Grigoroudis, E., & Matsatsinis, N. (2011). After testing it was decided that it would a beneficial addition. However, since the formula they provided was specific to the case included in their paper, a new formula and algorithm were developed that would apply to a broader range of situations.

As with BTL, BTL ds should in theory be more applicable to frequently purchased items.

Professor Paul Green’s Alpha rule is another rule that had earlier applications outside of conjoint analysis - such as in Urban and Silk's ASSESSOR pre-test market model. Alpha was added to Metrisim in July 2025.

In reality, it isn't a rule on its own, it is an exponent added to the utilities when calculating shares using the BTL or BTL ds rule. It has the effect of increasing the variance of the share percentages – the larger the alpha, the closer to the Maximum Utility rule.

An automatic search can be conducted between 0.5 and 3. This assumes that target.csv contains actual market shares (not manually entered calibration weights) – and as usual do not include percentage symbols. It automatically excludes none and recalculates shares to sum to 100 without none – since alpha was introduced before none estimation was possible and the main reason for alpha is to improve the accuracy of the ratios of shares between brands.

Alternatively, alpha can be entered manually.

If you switch to Max. Utility it of course ignores alpha.  If you switch to BTL or BTL ds it resets to the default of 1.