For single agents as well as for agents in partnerships the probability for a sexual contact within one day needs to be estimated in dependency to all other characteristics of agents associated with the frequency of sexual contacts.
As surveys always adress actual sexual contacts there is a problem concerning the concensual nature of the activity. As the agents should be autonomous there is the need to implement an framework that seperates intention and action. In a very basic model each agents builds an intention – in this case a simple 0 or 1 decision – and communicates this intention to potential partners. If two agents match up on their intentions a sexual contact will be realized. As mentioned before, the available data only states the number of those realized contacts.
The case most easy to analyse is the stable partnership because there is only a 1:1 relation of potential sex partners and survey data informing about the frequency of sexual contacts exists. Consider two agents (A & B) which either have the intention (e.g. for agent A: S_{A} = 0) or not have the intention (e.g. S_{A} = 0) to have sex. If both agents share the intention there is a sexual contact – denote the probability of this event by a and notice that this probability can be estimated from the data. Furthermore this probability is the product of the probabilities that each agent has the intention to have sex (a = P(S_{A} = 1) × P(S_{B} = 1)).
Table: Probability of agents in partnership for sexual contact under the assumption of symmetric
intention.
S_{A} = 1 | S_{A} = 0 | ||
S_{B} = 1 | a | b | P(S_{B} = 1) |
S_{B} = 0 | c | d | 1-P(S_{B} = 1) |
P(S_{A} = 1) | 1-P(S_{A} = 1) |
However to deduce marginal probabilities (P(S_{x})) as well as the agent behavior further assumptions are needed. A strong assumption is: The agents are symmetric in their intentions or P(S_{A} = 1) = P(S_{B} = 1). However this allows for a simple and immediate derivation of the marginal probabilities. Note that P(S_{A} = 0) = 1-P(S_{A} = 1) as there are only two options — then:
a = P(S_{A} = 1) × P(S_{B} = 1) => P(S_{A} = 1) = P(S_{B} = 1) = √a => P(S_{A} = 0) = P(S_{B} = 0) = 1-√a
This means that the probability for the intention for a sexual contact is equal to the squareroot of the probability of realized sexual contacts.