Copy-the-majority of instances or individuals? Two approaches to the majority and their consequences for conformist decision-making

Abstract

Cultural evolution is the product of the psychological mechanisms that underlie individual decision making. One commonly studied learning mechanism is a disproportionate preference for majority opinions, known as conformist transmission. While most theoretical and experimental work approaches the majority in terms of the number of individuals that perform a behaviour or hold a belief, some recent experimental studies approach the majority in terms of the number of instances a behaviour is performed. Here, we use a mathematical model to show that disagreement between these two notions of the majority can arise when behavioural variants are performed at different rates, with different salience or in different contexts (variant overrepresentation) and when a subset of the population act as demonstrators to the whole population (model biases). We also show that because conformist transmission changes the distribution of behaviours in a population, how observers approach the majority can cause populations to diverge, and that this can happen even when the two approaches to the majority agree with regards to which behaviour is in the majority. We discuss these results in light of existing findings, ranging from political extremism on twitter to studies of animal foraging behaviour. We conclude that the factors we considered (variant overrepresentation and model biases) are plausibly widespread. As such, it is important to understand how individuals approach the majority in order to understand the effects of majority influence in cultural evolution.

Fig 1

(A) As the proportion of individuals that perform behaviour A (p) increases so does the proportion of instances of a behaviour being performed that are behaviour A (p_i). However, the rate of increase is strongly affected by the rate at which each individual performs behaviours A or B (r). When behaviour A is performed more frequently than behaviour B (r > 1) p_i increases rapidly when p is low, but this soon slows down as p reaches moderately high values because p_i approaches 1. When A is performed less frequently than B (r < 1) the increase in p_i is slow at first, but once p reaches moderately high values it speeds up dramatically. (B) The probability that two observers who count individuals and instances, respectively, will disagree over which behaviour is in the majority is minimized when r = 1, but as r increases or decreases, the probability rapidly increases, slowing down as it reaches a maximum value of 1. Note the x-axis is logarithmic to make the symmetry around r = 1 more apparent.

Fig 2. Depending on the starting composition of the population, the two approaches to the majority can either lead to the populations converging on the same behaviour (green lines) or diverging.

In the latter case this can be because the two approaches produce disagreement over which option is in the majority (red lines) or because even though the two approaches agree over which option is in the majority they nonetheless disagree sufficiently over the size of this majority (yellow lines). In the case shown r = 1.5 and s = 1.5 and the lower boundary of the yellow region is 8/35.

Fig 3. The effect of the number of demonstrators (n), the frequency of behaviour A (p), the rate of performance of A relative to B (r) and the overrepresentation of A among demonstrators (r_d) on the probability that two observers who counted individuals and instances, respectively, would disagree over which behaviour is in the majority.

(A-B) Certain values of p are associated with a raised probability of disagreement. The range of this region increases as r diverges from 1. As n increases, the probability of disagreement within this region approaches 1, while, outside of it, it approaches 0. For lower values of n the probability is more diffuse, being lower within the region, but higher outside of it. (C-D) Introducing a systematic bias into the demonstrators shifts the values of p that are associated with a high probability of disagreement (r is set to 3 in both panels), but the effect of n remains the same as in panels A-B.