Over the past year, India has witnessed an upheaval of sexual harassment and assault allegations through social media and anonymous reporting. More recently, women from the media, performing arts and other professions have come forward with accounts of inappropriate conduct and sexual harassment at the hands of ‘powerful’ men.

This article draws from game theory and behavioural science to understand this in greater detail. Necessarily, the resulting analysis is limited by many assumptions and caveats, but aims to provide nuance to this widely-reported behaviour.

Consider a two-person sequential game, where a male in the first stage chooses between two actions: Harass (H), or do not harass (NH) a woman. In both cases, the woman has two subsequent choices—report (R), or do not report (NR). We consider reporting to be disclosing to the public, which could include posting on social media, filing a formal complaint with officials, or to an internal complaints committee.

Now, consider all four combinations: The game terminates in two cases, both when the woman chooses NR. The simplest case (intuitively), is the one where the man chooses NH and the woman chooses NR, where they are both neither better nor worse off. However, when the man chooses H and the woman chooses NR, she undergoes significant emotional and mental damage, and therefore, a negative payoff. The man receives a positive payoff, as he is assumed to derive utility from harassing women.

There are various reasons why women may choose not to report an incident of sexual harassment. It could be on account of pluralistic ignorance: A woman considering R is deterred because she wrongly believes that all other women also strictly prefer NR to R.

The man will always choose to harass women since the onus is on them to prove the allegations-

When a woman chooses R, preceded by NH (i.e. a false allegation), both face a negative payoff (more so for the man than the woman owing to the reputational damage); but when preceded by H, both face an equally negative payoff. H followed by R damages potential economic opportunities for a man, but also costs the woman who is seen with suspicion, potentially deprived of employment, or stigmatized by reliving the incident ad nauseam.

When she chooses R, males can choose two actions: To either Admit (A), or to Fight the allegation (F). The game continues if and only if the man chooses F, following which the game places the responsibility squarely on the woman to either Prove (P) or remain Unproven (UP). Again, consider the two points at which the game terminates: When the male chooses to admit (A). However, if he plays A when the allegations are true, then he faces the same negative payoff as he would if he chose F—i.e. the man is indifferent between fighting and admitting when he has actually harassed the woman.

Thus, when considering his actions between A and F, we assume that he gains more utility when the woman he has harassed gets a lower payoff. In the case where R is preceded by NH, the man prefers F strictly to A, since the costs associated with F are not nearly as high as the reputational and emotional damage to him if he admitted a false allegation.

Assuming that this game is played out in a patriarchal society, the onus is on women to prove their allegations true. Whether or not she was harassed, the woman strictly prefers being able to prove (P) her allegations than letting them remain unproven.

However, the costs to being unproven are significantly higher in the H case. She receives the highest negative payoff, whereas the man regains some positive payoff by coming out of an investigation without any charges being proved. If they are proved, in both H and NH, the man faces the highest negative payoff, since along with incurring costs in fighting the case, he is now known to the public as a harasser and potentially faces criminal action.

Finally, the subgame perfect equilibrium of this game suggests a solution that resonates with what has been unfolding on social media. For men, action H strictly dominates NH, since he knows that a woman will strictly prefer NR to R. Since the game assumes common knowledge, common and perfect information, all players know exactly how the game will play out and, hence, choose their dominant strategy. The man will always choose to harass women because he knows that she knows the onus is on them to prove their allegations, which she will have to do, since the man always prefers to fight allegations than simply admit to them, regardless of whether he has actually harassed her or not.

This analysis is aimed to be a bare-bones attempt at clarifying the gender roles at play while dealing with cases of sexual harassment.

For a more detailed analysis that considers delays in reporting, anonymous reporting by multiple women, and corroboration, refer to Frances Xu Lee and Wing Suen’s working paper ‘Credibility of Crime Allegations’. Their elegant economic model explains repeat offences and delays in reporting of sexual misconduct. It suggests using a novel online system called ‘Callisto’ to discretely and privately transmit reports of sexual harassment, applied to the case of academic institutions. This must be considered in developing countries like India where stigma still remains the prime hurdle in reporting sexual harassment.

Anirudh Tagat is a research author at the department of economics, Monk Prayogshala.

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