MaxDiff (Maximum Difference Scaling, or best-worst scaling) measures how much people prefer a list of items. Respondents see small sets of items and pick the best and worst in each. Because every item appears in many sets, MaxDiff produces a far more discriminating ranking than a standard rating scale, and avoids scale-use bias (everything rated “very important”).
Counting analysis
The simplest summary. For each item, count how often it was chosen best vs worst, relative to how often it was shown:
B−W score = (times Best − times Worst) / times Shown
The score runs from −1 (always worst) to +1 (always best). We rescale it 0 to 100 (best item → 100) for an at-a-glance ranking. Counting is fast and intuitive but does not yield a probabilistic model.
Aggregate logit utilities
For statistically grounded scores we fit a multinomial-logit choice model to all of the best and worst choices by maximum likelihood. In each task, the best pick is modeled as a logit over the shown items, and the worst pick as a logit over the negated utilities:
P(best = i) = e^uᵢ / Σⱼ e^uⱼ P(worst = i) = e^(−uᵢ) / Σⱼ e^(−uⱼ)
The combined log-likelihood is concave, so it has a single maximum, which we find by Newton-Raphson (one item’s utility is fixed at 0 for identification). Standard errors come from the inverse information matrix at the solution.
Preference shares
Utilities are turned into the share of preference each item would win against the others (a softmax):
Share(i) = 100 × e^uᵢ / Σⱼ e^uⱼ: sums to 100% across items.
Scope & caveats
This is an aggregate (whole-sample) analysis: it does not estimate individual-level utilities (Hierarchical Bayes). If an item is almost always chosen best (or never worst), its utility is mathematically unbounded; the fit caps its iterations and flags the item rather than reporting an infinite value. Everything runs locally in your browser: your raw data never leaves the device.