Qual Quant (2007) 41:557–568
Of songs and men: a model for multiple choice with
Christian Borghesi · Jean-Philippe Bouchaud
Published online: 3 March 2007
© Springer Science + Business Media B.V. 2007
Abstract We propose a generic model for multiple choice situations in the presence
of herding and compare it with recent empirical results from a Web-based music mar-
ket experiment. The model predicts a phase transition between a weak imitation phase
and a strong imitation, ‘fashion’ phase, where choices are driven by peer pressure and
the ranking of individual preferences is strongly distorted at the aggregate level. The
model can be calibrated to reproduce the main experimental results of Salganik et al.
(Science, 311, 854–856 (2006)); we show in particular that the value of the social inﬂu-
ence parameter can be estimated from the data. In one of the experimental situation,
this value is found to be close to the critical value of the model.
Keywords Herding · Social Inﬂuence · Random Field Ising Model
Making decisions is part of everyday life. Some situations require a binary choice (i.e.
to vote yes or no in a referendum, to buy or not to buy a cell phone, to join or not to join
ariot,etc.Schelling 1978; Granovetter 1978). Many others involve multiple options,
for example in the ﬁrst round of French presidential elections (where the number
of candidates is typically 15), in portfolio management where very many stocks are
eligible, in supermarkets where the number of possible products to buy is large, etc.
In most cases, the choice is constrained by some generalized budget constraint,either
C. Borghesi · J-P. Bouchand
Service de Physique de l’État Condensé, Orme des Merisiers, CEA Saclay, Gif sur Yvette Cedex,
J-P. Bouchand (
Science & Finance, Capital Fund Management, 6-8 Bd Haussmann, 75009 Paris, France