Who Should Make the First Move?

Water doesn’t flow under a stone that lies still.

— Russian proverb

In a durable cultural script one person proposes and the other chooses. The first risks a refusal, the second keeps the right to judge. That makes the waiting role look stronger: people come to them, they decide. In 1962 David Gale and Lloyd Shapley showed that under a particular procedure it works the other way round. Their problem was not about dating. Applicants had to be assigned to colleges so that no applicant–college pair was left who would both prefer each other to their current assignment. Such an assignment is called stable. The algorithm is simple. One side makes offers in order of preference. The receiver provisionally holds the best offer and rejects the rest. Those rejected move on to their next option. The process ends when there are no new offers.

For finite two-sided sets with complete strict preferences the algorithm always ends in a stable matching. In this setting the outcome is the best among stable ones for the proposing side and the worst for the receiving side. Incomplete lists, ties, changing preferences and other definitions of stability require extra rules and can change the properties of the result.

The advantage of the first move

The proposer’s advantage comes from the order of moves. He starts with his favourite option and descends only after a refusal. The receiver sees only those who turned up and picks among them. Her best possible partner may never make an offer, because he was locked into another pair earlier. In the algorithm the passive side holds the right of refusal but does not control the set of options arriving. The initiator shapes his own sequence of attempts. This resembles ordinary life. A person who does the inviting chooses whom to give a chance. Someone who only responds selects from a sample formed by someone else’s initiative.

The formula “let them pursue me” keeps control over the individual answer and hands control over the incoming flow to others.

It is easy to draw one conclusion too many from the algorithm: since in the traditional script men do the proposing, the mathematics seems to prove their advantage as a sex. The precise result is different: under deferred acceptance the proposing side gets, for each of its members, the best option among all stable assignments, and the receiving side the worst among the stable ones. This does not mean that every proposer gets the partner he wants, or that initiative always pays outside the procedure. The result lives inside strict conditions — fixed preferences, a complete set of participants, a centralised algorithm and the goal of a stable assignment. In dating there is no dispatcher, people don’t see everyone, they change preferences, come back and learn. The more modest conclusion survives: initiative affects the composition of the options you can reach.

The one who walks the room

An organisational detail of speed dating hands out the roles. Usually the men move from table to table and the women stay put. The one who walks physically approaches, starts each new contact, and performs a small act of choosing many times over; the one who sits waits and judges whoever appears in front of them.

Eastwick and Finkel changed the arrangement: sometimes the men rotated, sometimes the women. In the usual setup the women looked more selective. When the women rotated, the difference disappeared; the moving side generally became less selective and more confident in its own romantic appeal. A few steps across a room shifted an effect usually read as a stable property of sex.

The sample consisted of young people at short events, so the experiment speaks about initial attraction within that procedure, not about the whole history of choosing a partner. Within those limits the causal contribution of the role is clearly visible: changing who gets up and walks over weakened a sex difference that looked stable.

The algorithm and the room show two different advantages of initiative. In a stable assignment the proposer states preferences earlier and gets the best of the available stable outcomes. On a date the action also changes the state of the person acting: it strengthens the sense of choosing and brings a yes psychologically closer. Both mechanisms make passivity an active constraint rather than neutral waiting.

The traditional heterosexual script, where the man proposes and the woman chooses, does more than distribute the risk of refusal. It trains the participants in different skills. One practises noticing interest and surviving rejection; the other practises sorting incoming offers and wondering whether her own initiative was obvious enough. When the norm changes, so do the number of offers and the mix of people making them.

The price of a refusal

Norms often assign initiative to one side because an offer has a price. A refusal causes embarrassment and can affect reputation. In some cultures female initiative was read as sexual availability; male passivity as weakness. Physical risk and the risk of being stalked are also distributed asymmetrically. The norm may not have been a simple error of calculation but a way of organising behaviour under old threats and roles. When conditions change, the norm outlives its basis. A woman gets an education, an income and contraception, and goes on waiting so as not to break the script. A man doesn’t want to be the only initiator, but reads a woman’s silence as a lack of interest. Two people sensibly follow the rule and jointly produce the absence of a meeting.

This is a coordination problem. Each waits for a signal the other also considers improper or risky to send.

The first move need not be a declaration or a large bet. Its function is to get an answer. An invitation to a short meeting converts uncertainty into observation. A refusal closes one option; a yes opens the next stage. A reversible, concrete step costs less. Here it is worth distinguishing initiative from pursuit. After a rejection the Gale–Shapley algorithm sends the participant to his next option. It does not advise repeating the offer until the receiving side gets tired. A refusal is information, not the opening of negotiations about the right to refuse. Activity enlarges the set of attempts; it grants no right to the desired result.

The one who waits chooses from a flow shaped by someone else’s nerve, visibility, reading of signals and willingness to risk a refusal. Such a flow is far from a random or an obviously better sample. Initiative especially widens the options of those whom the cultural script makes invisible as initiators: women in traditional roles, shy men, people in same-sex dating with no positions assigned in advance.

The first move does not deliver the best person by theorem. It gives a different advantage: a part in creating the set you will then have to choose from. The right to say no stays with both and matters no less than the right to phrase the offer.

Key sources

Gale, D., & Shapley, L. S. (1962). College admissions and the stability of marriage. American Mathematical Monthly, 69(1), 9–15.

Roth, A. E. (2008). Deferred acceptance algorithms. International Journal of Game Theory, 36, 537–569.

Finkel, E. J., & Eastwick, P. W. (2009). Arbitrary social norms influence sex differences in romantic selectivity. Psychological Science, 20(10), 1290–1295.