MaxDiff

The MaxDiff is a long-established theory in mathematical psychology with very specific assumptions about how people make choices: it assumes that respondents evaluate all possible pairs of items within the displayed set and choose the pair that reflects the maximum difference in preference or importance. It may be thought of as a variation of the method of Paired Comparisons. Consider a set in which a respondent evaluates four items: A, B, C and D. If the respondent says that A is best and D is worst, these two responses inform us on five of six possible implied paired comparisons:

$A > B$
$A > C$
$A > D$
$B > D$
$C > D$

The only paired comparison that cannot be inferred is B vs. C. In a choice, like above, with four items MaxDiff questioning informs on five of six implied paired comparisons. In a choice among five items, MaxDiff questioning informs on seven of ten implied paired comparisons.

The total amount of known relations between items, can be mathematically expressed as follows: $(2(N-1))-1)$ . $N$ represents here the total amount of items. The formula, makes it clear that the effectiveness of this method, of assuming relations, drastically decreases as $N$ grows bigger.

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