Part-worth utilities are hard to act on by themselves. A market simulator turns them into the questions a pricing or product team actually asks: if we launch this, at that price, against those competitors, how many people choose us? This guide explains how simulators work, how to read their outputs, and where their limits are.
What a simulator does
A simulator takes each respondent's estimated part-worths and a scenario you define: a set of products, each described by its attribute levels and price. It adds up the part-worths to get each respondent's utility for each product, applies a choice rule to turn utilities into choices, and averages across respondents. Change the scenario and the shares update. Because the part-worths are estimated per respondent, the same scenario can be read for the whole sample or for any segment.
Choice rules
First choice
Each respondent is assigned to the product with the highest utility. It is simple and largely avoids the IIA problem described below, but it tends to exaggerate differences between products and needs larger samples to be stable (Sawtooth Software, Market Simulator Models).
Share of preference (logit)
Each respondent's choice is split across products in proportion to the exponential of their utility:
$$s_{ij} = \frac{e^{U_{ij}}}{\sum_{k} e^{U_{ik}}}$$
where $U_{ij}$ is respondent $i$'s utility for product $j$. The shares are then averaged across respondents. This is the multinomial logit rule the model was estimated with, so it is consistent with the estimation and gives smooth responses to small changes.
Randomized first choice
Randomized first choice (RFC) adds random error to the utilities and repeats first-choice simulations many times. It was developed to correct for product similarity, and Sawtooth reports that it has outperformed the other rules on holdout tests (Sawtooth Software, Market Simulator Models).
Which Ordeen uses
Ordeen uses share of preference: a logit share for each respondent, from their own part-worths, averaged across the sample or segment. Because the estimates come from Hierarchical Bayes, Ordeen also repeats the simulation across posterior draws and shows a 95% credible interval for each share, plus the probability that each product is the most preferred.
The None option and total demand
Shares that always add to 100% hide an important question: would people buy anything at all? If your study includes a None option, each respondent has a utility for walking away, and the simulator includes it as one more alternative. Raising every price then shows some people leaving the category rather than switching, which is closer to how demand actually behaves. Ordeen uses each respondent's own None utility where one was estimated.
Price scenarios
The share curve
Set a product's price and the simulator returns its share. Repeat across many prices and you get a share curve: share of preference as a function of price, holding every competitor fixed. Ordeen draws this curve from half your lowest tested price to one and a half times your highest, and marks the price levels in your design on it. The stretches beyond your lowest and highest levels are extrapolations; see the limits below.
One step up or down the ladder
The most useful single reading is often the simplest: what happens to share if we move one price level up or down? Ordeen reports the change in share points and in percent for each step, so you can see where demand is flat and where it falls away.
Elasticity
Price elasticity summarises the same curve as a ratio:
$$\varepsilon = \frac{\%\,\Delta\,\text{share}}{\%\,\Delta\,\text{price}}$$
An elasticity of −2 means a 1% price rise loses about 2% of share. Ordeen reports elasticity at your current price.
Why there is no single "optimal price"
Share alone cannot tell you the best price, because the best price depends on your margins. A product can win share at a price that loses money. Ordeen therefore does not label any price as optimal. If you add unit costs to the products in a scenario, it reports expected margin (share × (price − cost)) alongside share, so the trade-off is visible.
Willingness to pay
The ratio method
With a price attribute in the design, a utility difference can be converted into money by dividing it by the price coefficient:
$$\text{WTP}_{\ell} = \frac{u_{\ell} - u_{\text{ref}}}{\lvert \beta_{\text{price}} \rvert}$$
where $u_{\ell}$ is the part-worth of level $\ell$ and $u_{\text{ref}}$ is the reference level. Ordeen uses the lowest-utility level of each attribute as the reference, so WTP reads as "how much more people would pay for this level than for the least preferred one".
Intervals
A WTP figure is a ratio of two uncertain quantities, so it needs an interval. Krinsky and Robb (1986) proposed drawing the parameters many times from their estimated distribution, computing the ratio for each draw and taking percentiles. With Hierarchical Bayes the posterior draws already provide those samples, and Ordeen calculates its WTP intervals from them. If the price coefficient's interval includes zero, the ratio is undefined and Ordeen does not report a WTP rather than show a misleading number.
SKU line-ups with TURF
When you can only stock a few variants, the question changes from "which product wins" to "which set of products reaches the most people". TURF (total unduplicated reach and frequency) answers it. Ordeen counts a respondent as reached when one of your products is their first choice in the scenario, then builds the line-up greedily: it adds the product that brings in the most new people, and stops when the next addition adds less than two points of reach or the line-up reaches five products. The result shows how quickly reach saturates, which is often the strongest argument against an extra SKU.
Competitor scenarios
Every share is relative to the competitors in the scenario. Build the base case from the products your customers actually see, at their current prices, and check that the base-case shares look plausible before testing changes. In Ordeen, the competitors listed in your brief can seed the first scenario.
Limits to keep in mind
IIA
The logit rule assumes independence of irrelevant alternatives (IIA): adding a product takes share from all others in proportion to their current share, even if the new product is a near-copy of one of them (Train, 2009, ch. 3). Sawtooth notes that the problem is much reduced when shares are computed from individual-level part-worths, as they are here, but it is worth remembering when you simulate two very similar products.
Share of preference is not market share
Simulated shares assume full awareness, full distribution and a purchase decision made from exactly the products in the scenario. Real markets have none of these. Use simulator shares to compare scenarios with each other, and calibrate to actual sales before treating them as volume forecasts.
Stay within the tested range
The model only knows about prices and levels that respondents saw. Results between tested price levels are interpolations and usually safe to read. Results beyond the lowest or highest level assume the price response carries on in the same shape, which nothing in the data confirms. If the commercially interesting price is outside the range, test it in the next study.
References
Sawtooth Software. Market Simulator Models. Lighthouse Studio Manual. sawtoothsoftware.com
Train, K. E. (2009). Discrete Choice Methods with Simulation, 2nd ed. Cambridge University Press. Chapter 3, Logit. eml.berkeley.edu
Krinsky, I. and Robb, A. L. (1986). On Approximating the Statistical Properties of Elasticities. Review of Economics and Statistics 68(4), 715–719. doi:10.2307/1924536
Orme, B. (2019). Getting Started with Conjoint Analysis, 4th ed. Research Publishers LLC.
