Attraction Model

An attraction model is a class of market-share models built on a simple, powerful idea: a brand's market share equals its own attraction divided by the sum of the attractions of all the competing brands. Each brand is assigned an attraction — a number reflecting how appealing it is to buyers, usually built from marketing variables like price, advertising, distribution, and product attributes — and its predicted share is just its attraction as a proportion of the total attraction in the market. The best-known form is the multiplicative competitive interaction (MCI) model, where a brand's attraction is the product of its marketing variables raised to estimated powers; a related form uses an exponential (multinomial logit) specification. In every case the share is the brand's attraction over the sum of all attractions, which is what makes it an attraction model.

Attraction models matter because the share-equals-attraction-over-total-attraction structure has a property that simpler share models lack: it is logically consistent by construction. Because each share is a positive attraction divided by the sum of all positive attractions, every predicted share automatically falls between zero and one, and all the brands' shares sum to exactly one — exactly what real market shares must do. This is not guaranteed in naïve linear share models, which can predict negative shares or shares above one, or shares that do not sum to the market. By embedding the logical constraints of shares directly into the model's form, attraction models give predictions that always behave like real shares. That consistency, plus their ability to capture how brands' marketing efforts compete for a fixed total of demand, is why they are a standard tool in market-share analysis.

The defining virtue of an attraction model is what is called logical consistency, and it follows directly from the share-equals-attraction-over-total-attraction form. If every brand's attraction is a positive number, then dividing one brand's attraction by the sum of all of them must produce a value greater than zero and less than one — a valid share. And since each share is that brand's slice of the same total, the slices necessarily add up to the whole, so the shares sum to one. The model cannot produce a negative share or a share above a hundred percent, because its very structure forbids it. This is a meaningful advantage: a share model that can predict impossible shares is unreliable, and attraction models rule those impossibilities out by design rather than by patching them afterward.

This sets attraction models apart from simpler alternatives. A linear regression of share on marketing variables can fit the data in a range yet predict shares below zero or above one when pushed, and its predicted shares need not sum to the market — logically impossible results that have to be hand-corrected. Attraction models avoid this because the constraint is built into the functional form, not bolted on. The trade-off is that attraction models are non-linear and somewhat more complex to estimate, and like all models they depend on choosing the right attraction variables and on the assumption that share really does behave as relative attraction. But for modelling how competing brands split a market according to their marketing efforts, the combination of logical consistency and a clear competitive interpretation makes the attraction model a natural and widely used choice.

Using an attraction model well means treating it as a logically consistent way to model market share — each brand's share as its attraction over the total attraction — and choosing the attraction specification, such as the multiplicative competitive interaction form, that fits how the market actually competes. It means building each brand's attraction from the marketing variables that genuinely drive choice (price, advertising, distribution, product attributes), estimating the model carefully, and using it to understand and predict how shifts in those variables would redistribute share among competitors. Because the form guarantees shares between zero and one that sum to the market, the predictions stay sensible, which makes the model useful for competitive what-if analysis. As always, the realism of the inputs and the appropriateness of the attraction form matter as much as the elegant structure.

The failures are using a naïve linear share model that can predict impossible shares (the very problem attraction models exist to avoid), specifying attraction from the wrong variables or with the wrong functional form, treating the model's logical consistency as if it guaranteed predictive accuracy (consistency of shares is not the same as correctness of forecasts), and over-trusting the model without validating it against real market behaviour. The discipline is to use the attraction model for what it does well — producing logically consistent shares from a clear competitive structure — while specifying its attractions thoughtfully, estimating it soundly, and validating its predictions, so its elegant guarantee of valid shares is matched by inputs and assumptions that make those shares believable.

An attraction model — where a brand's share equals its attraction over the sum of all brands' attractions, as in the MCI model — yields logically consistent market shares between zero and one by construction.

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