How an Economist sees the Dating Market

Wikipedia defines dating as follows: Dating is a stage of romantic relationships in humans whereby two people meet socially with the aim of each assessing the other’s suitability as a prospective partner in an intimate relationship or marriage.

Before we continue, please review the following disclaimers and assumptions.

Disclaimers:

Assumptions:

If any of these assumptions seem unrealistic to you, then the entire model will fail to withstand your scrutiny.

In order to describe the model, we will first need to develop some concepts from Economics. To make the discussion easier, I will introduce some notation. “Choosers” will refer to individuals evaluating a partner to date, and “options” will refer to the partners being evaluated. Of course, people in the dating market are both choosers and options since both parties will have to consent to date each other, but when discussing the perspective of choosers we will consider only one side of the market choosing the other, such as women choosing from male options.

The first fundamental idea is that people can establish a sense of value when evaluating a potential date, and that this sense of value can be condensed into a single unit of value, for example we can say that an option on the dating market can be evaluated and assigned some number of “dating points” according to various attributes this option possesses. These dating points may be evaluated uniquely for each person doing the evaluation, so chooser X may evaluate option Y and assign them x dating points, while chooser Z may evaluate the same option Y but assign them a different number of dating points z. A critical extension of the dating points concept is that then we can rank our dating preferences such that if chooser Y evaluates option X to have m dating points and option Z to have n dating points, where m > n, then chooser Y would prefer to date X than to date Z. This is a formal statement of the simpler concept that given two (or more) choices of potential people to date, people are likely to have some preference among the choices based on differences between the attributes of the choices.

The second fundamental idea pertains to the way people differ among attributes and how choosers rank those attributes. To do this we will use a non-dating example and introduce two new economic terms called “Vertical Differentiation” and “Horizontal Differentiation”.

Consider evaluating a car for purchase. There are many different features associated with a car such as, speed, acceleration, horsepower, environmental impact, reliability, car style, car color, etc. In general, almost everyone will agree that higher ratings of speed, acceleration, and reliability will be better than lower ratings of speed, acceleration, and reliability. Similarly, everyone will generally agree that a low environmental impact is better than a high environmental impact. However, not everyone will agree that a certain car color is better than another car color (is black obviously better than blue?), or that a certain car style is inherently better than another (is a Toyota Corolla’s design inherently better than a Honda Civic’s design?). The qualities that everyone can agree on — speed, acceleration, reliability, environmental impact — are classified as being vertically differentiated, i.e. everyone at a market level can agree these are desirable qualities and on their appropriate directions (lower or higher), whereas the qualities that people can’t find consensus on — color, car design — are described as horizontally differentiated. These two terms describe behavior at the market level but do not describe the magnitude of individual preferences for these attributes. For instance, someone might be willing to trade off a certain amount of horsepower for a specified lower environmental impact, but everyone would agree these are both desirable things.

Now back to dating markets.

Dating markets are vertically and horizontally differentiated; there are attributes that all choosers agree are desirable of options and attributes for which choosers disagree on desirability. To make this more concrete, all choosers will likely agree that a high rating on something like social intelligence is more preferable in an option than a low rating, whereas some choosers will agree that an option who is into spectator sports is desirable while other choosers will disagree. The categorization of specific attributes into the vertically differentiated category and into the horizontally differentiated category is a detail which may be up for debate, but I will attempt to make a case for a list of attributes that fall into the vertically differentiated category using data and the academic literature later in another article.

We now combine the two economic concepts we describe above to generate a description of how the dating market works. For any chooser evaluating any option i, the chooser is evaluating the option along two criteria, a value for the vertically differentiated attributes, vᵢ, and a value for the horizontally differentiated attributes, hᵢ, and the number of dating points the chooser assigns to option i is given by vᵢ + hᵢ. A chooser can then do this for any set of presented options and generate a preference list among that set.

Hold aside practical considerations for the moment and imagine, then, that we can do this for all choosers evaluating all options and arrive at a series of these preference rankings corresponding to the number of choosers and the number of options available (specifically, number of choosers x the number of options x 2). The information contained in the sum of these preference rankings defines the dating market: we can use this information to determine an aggregate value for all of our vertically differentiated attributes, since these allow for comparison. Let’s unpack this a little.

The above plot shows that women have a preference for men who are their height or taller as demonstrated by the number of times women of various heights “Like” profiles of men of various heights.

The second plot echoes the first but adds an additional dimension, not only do women like men who are taller than themselves, the number of likes scales as the man gets taller. In other words, height is a vertically differentiated good when women evaluate men, so taller is better for men when viewed as an option.

From our set of all preference lists with corresponding vᵢ’s, we can calculate the marginal increase in dating points that an inch of height gives to a male option on the dating market relative to some baseline. We can do this for all our vertically differentiated attributes and give our options a composite market level value of their vertical attributes. So at a market level, any male option i can be assigned a value, vᵢ*, that corresponds to his market level vertical value as the sum of all the individual values of all his vertically differentiated attributes. We can do this similarly for men as choosers evaluating women as options on their vertically differentiated attributes.

To keep this digestible, we will now do two things before continuing. The first is that we will build up this model very slowly, adding additional complications as we go. The second is that we will limit the market to 100 men and 100 women in order to make it easier to think about how these interactions might actually play out, rather than thinking about the real world situation of thousands or millions of market participants.

Based on our analysis as described, we now have market values for the vertical differentiation of each of our groups of options, i.e. men and women. There are potentially a lot of ways we can match people in this market but we will consider three ways we can use our model to go about matching these 100 men and 100 women in our micro-market when considering only vertical differentiation:

These have their problems however, with (1) and (2) having largely similar problems. In the case of the first two, these preference lists are tailored to the individual chooser, not at a market level, so each of these unique preference functions (one chooser may value an inch of height, for instance, more than another chooser) will generate a different list and the matchings will be good for the side of the market the preference list is being based off, but it may be bad for the other side being matched. Given that one of our assumptions is self-awareness, this may lead to non-consent for some number of matches if the matches are too far apart.

Assortative matching has some problems as well. Specifically, we are using market level valuations rather than a chooser’s individual preference list, which may rank another option more highly than the option that corresponds to the chooser’s market rank. In practice this may be a small concern, however, since the option that is more highly ranked may have the chooser at a low rank. Again, the impact of our system that not only must one choose, but one must be chosen will tend to reinforce similar rankings. Based on testament from behavioral economist Dan Ariely in a video titled “Who you find attractive is based on how hot you are”, it seems that the assortative matching model may indeed be more accurate as they find people respond similarly in the real world.

Assortative matching will potentially play out as follows: Choosers evaluate their options and approach their highest preference. Since the market values are developed by the preferences of these choosers, most choosers should agree on who the highest valued options are and approach this subset of the options. The choosers in this subset will then see the value of the options approaching them and make a selection of the highest value from the pool, thus removing them from the pool available to match. The approaching choosers will then move onto their next ranked preference and the process will continue. Through this process, matches may not be as assortative as #n’s pair together, but rather may be more along the lines of participants in a neighborhood of each other’s ranking will pair.

Using Ariely as a certification of the assortative matching model for a market with only vertical differentiation and the argument above, we will assert that this model best describes real world behavior in this type of market.

Horizontally differentiated attributes are easier to understand, but may be difficult to work with/search over from a mathematical perspective, and definitely from an economics one. Since horizontal values are unique to each person’s preference function and do not scale across the market, it is not possible to generate a meaningful aggregate value for them. Moreover, there may be so many of these horizontal dimensions that it is not possible to aggregate them in a meaningful way at all. For a sample of what these sorts of horizontal preferences might look like, consider the following:

All of these and more would make up horizontal valuations of options. To make it more concrete, perhaps a chooser is fluent in both English and Chinese and they value someone who is also fluent in English and Chinese but would be happy with someone who is only able to speak English. In a market where the native language is English, additional fluency in Chinese may not be relevant at all to most other market participants, so this fluency is uniquely valuable to this chooser. This is what makes horizontally differentiated attributes difficult to incorporate into our model from a mathematical point of view. So how do we think about this model?

First, let us make a simplifying assumption for this iteration of the model that there is perfect information so it costs nothing to obtain information about the horizontal values of options, a chooser can just look at an option and know what their horizontal value is. There are two main possibilities here depending on the size of the horizontal values as compared to the size of the vertical values.

It is an empirical question how the size of valuation of vertical and horizontal attributes compare to each other. An astute reader may note here that according to Ariely, assortative matching seems to be how people in the real world behave in the dating market, and potentially conclude that, given this observation, it must be the case that vertical values are much larger than the horizontal ones so that our model behaves as (1) above, but this is premature. Specifically, we are assuming costless perfect information here, which is not at all true in the real world. Fortunately for us, when we develop our real world model next, it may not matter much how the sizes of valuation of the vertical and horizontal attributes compare.

This is the closest version of the model to the real world. In this model we have vertically and horizontally differentiated attributes as before, but now we introduce two things: screening costs and finite resources available to screen. Here’s how that works.

We will assume that vertically differentiated goods tend to be easy to observe, things like height, income, age, etc, while horizontally differentiated goods are difficult to observe. For instance, it is difficult to determine whether a chooser will have a fun conversation with an option simply by observing some easily available general information about the option, ultimately the chooser will simply need to test whether there is “chemistry” by interacting with the option, either in person or through some other medium; i.e. there is some screening cost to obtaining the horizontal value of an option, perhaps in time or money. Moreover, given that we don’t have infinite amounts of money or time (due to finite lifespan), we also have a finite amount of resources with which to spend on screening. So how do choosers evaluate options given easily observable vertical qualities, costly to observe horizontal qualities, and finite resources available for screening? One good strategy is assortative matching.

Through self-awareness, a chooser can get a sense of their own vertical value on the dating market and, through observation, can get a sense of the vertical value of any option being evaluated. Of course, every chooser wants to get a very high value match and avoid low value matches, but since we require consent the only way a chooser gets a high value match is if that high value option consents to match with the chooser. Consequently, we will generally see options reject propositions from lower vertically valued matches, even if they could potentially have high horizontal values, because to accept a proposition requires incurring the screening cost!

Imagine the following scenario in our 200 person micro-market: The #50 rank chooser propositions the #2 rank option. The #2 rank option does not know the horizontal value of the #50 rank chooser but has two possible responses, accept or reject. If the #2 rank option accepts, then they have to incur the screening cost and reduce the total number of potential screens they can do since they have finite resources, and the best outcome the option can hope for is that the #50 rank chooser has an incredibly high horizontal value, which will be difficult to know since it is not clear how to assess horizontal values. From the option’s perspective, the horizontal values may well be random. If the option rejects, then the option has, in effect, maintained the opportunity to screen another higher ranked chooser’s proposal and this is likely preferable given that accepting the proposal of a higher ranked chooser will guarantee a higher vertical value, thus making the value floor higher, i.e. the high vertical value will ensure that the overall value of the chooser is at least somewhat high. Given these conditions, and some assumptions around the actual magnitudes and distribution of vertical and horizontal values, screening costs, and screening budgets, it becomes clear that options will only accept proposals from — and make proposals to — similar or higher vertically valued options. However, since this behavior is symmetric when we flip the choosing and option groups, what we find is that people match at similar vertical values, i.e. assortative matching!

The model presented here is not perfect and most certainly not complete. It is built on a lot of assumptions about the size of values and cost of screening, etc, which all require empirical work to determine as well as further modeling to verify some of the statements. More than anything, it can be considered an early iteration of a hypothesis around how the dating market works with need for testing. All these caveats aside, I think it presents a model of the dating market that is useful in thinking about how people match today, how people might do better at their searching for a partner, and how economists and technology firms might think about how to make digital matching platforms more efficient.

There are still some big ideas to explore here. Namely, what are the vertically differentiated attributes for the two groups, what happens when there is an imbalance in the market, i.e. not a nice balanced 100 men and 100 women, and how do people behave in the real world outside of this “rational” economic model. These will be explored in other articles.

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