· The Strength of Absent Ties: Social Integration via Online Dating. We used to marry people to which we were somehow connected to: friends of friends, schoolmates, We used to marry people to which we were somehow connected to: friends of friends, schoolmates, neighbours. Since we were more connected to people similar to us, we were The Strength of Absent Ties: Social Integration via Online Dating By Philipp Hergovich and Josu e Ortega y First version: September 29, Revised: September 14, We used to The Strength of Absent Ties: Social Integration via Online Dating Josu e Ortega and Philipp Hergovich October 2, Abstract We used to marry people to which we were somehow We find that when a society benefits from previously absent ties, social integration occurs rapidly, even if the number of partners met online is small. Our findings are consistent with the sharp ... read more

Agents can only marry potential partners they know: i. if there exists a path of length at most k between them in the society graph. The length of the path is the number of such pairs. We consider two types of marriages:. Agents can only marry if they know each other. Agents can only marry if they know each other or if they have a mutual friend in common. We use the convention that agents that remain unmarried are matched to themselves.

Because realized romantic pairings are close to those predicted by stability Hitsch et al. A marriage μ is k -stable if there is no man-woman pair m , w who are not married to each other such that. Condition 8 is the only non-standard one in the matching literature, that ensures that a pair of agents cannot block a direct marriage if they are not connected in the corresponding graph, even if they prefer each other to their respective partner.

For any positive integer k , every Euclidean or assortative society has a unique k -stable marriage. For the Euclidean society, a simple algorithm computes the unique k -stable marriage. Let every person point to their preferred partner to whom they are connected to by a path of length at most k.

In case two people point to each other, marry them and remove them from the graph. Let everybody point to their new preferred partner to which they are connected to among those still left.

Again, marry those that choose each other, and repeat the procedure until no mutual pointing occurs. The procedure ends after at most r n 2 iterations. This algorithm is a minor modification of the one suggested by Holroyd et al.

The first one is equivalent to strict preferences, the second one is trivially satisfied. In their algorithm, agents point to the closest agent, independently if they are connected to them. The argument readily generalizes. Figure 5 shows the direct and long stable marriages for the Euclidean and assortative societies depicted in Figure 3.

We model online dating in a society S by increasing the number of interracial edges. We perform robustness checks in Appendix B , increasing both p and q but keeping its ratio fixed. younger people. Data shows that, from to , the percentage of people who use online dating has increased for people of all ages. While this occurs at a different rate, to obtain our main result we only need a small increase in the probability of interconnection for each agent.

S ϵ denotes a society that results after online dating has occurred in society S. S ϵ has exactly the same nodes as S , and all its edges, but potentially more. We say that the society S ϵ is an expansion of the society S. We want to understand how the welfare of a society changes after online dating becomes available, i. after a society becomes more interracially connected. We consider three welfare measures:.

Size , i. the total number of marriages in a society. Diversity , i. how many marriages are interracial. the ratio that obtains in a complete graph in expectation. Note that diversity may be above 1. Let R be a function that maps each agent to their race. A society is stronger whenever its marriages are between agents who are closer to each other.

A marriage with a small distance is better than one with a large one because is less susceptible to break up when random agents appear on the unit square, provided that the new outcome is to be k -stable too. The previous observation holds for assortative societies as well. Given a society S , the first question we ask is whether the welfare measures of a society always increase when its number of interracial edges grow, i.

when online dating becomes available. We refer to this property as edge monotonicity. It is well-known that when a new man joins a stable matching problem, every woman weakly improves, while every man becomes weakly worse off Theorems 5 in Kelso and Crawford, , 2. A welfare measure w is edge monotonic if, for any society S , and any of its extensions S ϵ , we have. If a welfare measure is edge monotonic it means that a society unambiguously becomes better off after becoming more interracially connected.

Diversity, strength, and size are all not edge monotonic. Before proving Proposition 2 , let us build some intuition about it. It may be surprising that the number of interracial marriages can decrease when more interracial edges are formed.

The intuition behind it is that a newly formed interracial edge may create one interracial marriage at the cost of destroying two existing ones, and the left-alone partners may now marry partners of their own race.

An interracial edge can similarly increase the average distance between couples if it provides a link between very desirable partners, i. those in the center for the case of Euclidean preferences. Those desirable partners are likely to drop their current spouses. The dropped agents now have to match with partners that have been dropped too, which are potentially further away from them.

Finally, size can be reduced if the new interracial edge links people who were already highly connected in the society, making them leave partners who are poorly so. The left-alone partners may now become unable to find a partner. To show that size is not edge monotonic, consider the society in Figure 3 and its direct stable matching in Figure 4 a. Remove all interracial edges: it is immediate that in the unique stable matching there are 4 couples now, one more than when interracial edges are present.

For the case of strength, consider a simple society in which all nodes share the same y -coordinate, as the one depicted in Figure 6. There are two intraracial marriages and the average Euclidean distance is 0.

When we add the interracial edge between the two central nodes, the closest nodes marry and the two far away nodes marry too. The average Euclidean distance in the expanded society increases to 0.

To show that diversity is not edge monotonic, consider Figure 7. There are two men and two women of each of two races a and b. In this extended society, there is just one interracial marriage, out of a total of three, when before we had two out of two.

The failure of edge monotonicity by our three welfare measures makes evident that to evaluate welfare changes in societies, we need to understand how welfare varies on an average society after introducing new interracial edges.

We develop this comparison in the next Section. A final comment on edge monotonicity. The fact that the size of a society is not edge monotonic, as shown in Proposition 2 , implies that adding interracial edges may not lead to a Pareto improvement for the society. Some agents may become worse off after the society becomes more connected. Nevertheless, the fraction of agents that becomes worse off after adding an extra edge is never more than one-half of the society.

Ortega discusses this phenomenon in detail and characterizes the associated welfare losses of those hurt by integration. In the last Section we found that our three welfare measures may increase or decrease after adding interracial edges. Therefore, we need to analyze what happens to welfare in expectation when agents become more connected.

There are two ways to answer this question. The first one is to provide analytical expressions for the expected welfare measures as a function of the number of interracial edges.

However, providing analytical solutions is incredibly complicated, if not impossible. The second way to approach the problem is to simulate several random societies and observe how their average welfare change when they become more connected. This is the route we follow. We create ten thousand random societies, and increase the expected number of interracial edges by increasing the parameter q.

In the following subsections, we describe the changes of our welfare measures for different values of q. The results for other values of p are similar and we present them in Appendix B. The Matlab code is available at www. We consider the following four scenarios:. Five races and long marriages, appears in yellow with cross markers ×.

In the case of long marriages, even the smallest increase in the probability of interracial connections in this case of 0. With either two or five races we obtain that diversity is exactly one.

For the cases with direct marriages, the increase in diversity is slower but still fast: an increase of q from 0 to 0. Echenique and Fryer find that the typical American public school student has 0. It is also a sensible assumption that p is large, given the clear residential segregation patterns in the U.

Cutler et al. Figure 7 b summarizes our main result, namely. Diversity is fully achieved with long marriages, even if the increase in interracial connections is arbitrarily small. With direct marriages, diversity is achieved partially but still substantially, so that an increase in q always yields an increase in diversity of a larger size, i. diversity is a concave function of q.

The intuition behind full diversity for the case of long marriages is that, once an agent obtains just one edge to any other race, he gains n 2 potential partners. The reader may think that the full diversity result heavily depends on each race being fully connected, i.

This is not the case. We obtain full diversity for many other values of p , as we discuss in Appendix B. When same-race agents are less interconnected within themselves, agents gain fewer connections once an interracial edge is created, but those fewer connections are relatively more valuable, because the agent had himself less potential partners before the creation of new interracial edges.

Result 1 implies that, assuming long marriages are formed, very few interracial links can lead a society to almost complete racial integration, and leads to very optimistic views on the role that dating platforms can play in the reduction of racial segregation in our society.

Our result is in sharp contrast to the one of Schelling , in its well-known models of residential segregation, in which a society always gets completely segregated. The number of interracial marriages should increase after the popularization of online dating.

A second observation, less pronounced that the increase in diversity, is that the strength of the society goes up when increasing q. For an illustration, see Figure 9 , which considers the same four cases as before in both Euclidean and assortative societies. It is clear that, for all combinations of parameters see Appendix B for further robustness checks , there is a consistent trend downwards in the average distance of partners after adding new interracial edges, and thus a consistent increase in strength of the societies.

We present this observation as our second result. Strength increases after the number of interracial edges increases.

The increase is faster whenever the society has more races, and converges to a higher level with long marriages. Assuming that marriages with a higher average distance have a higher chance to end up divorcing, because they are more susceptible to break up when new nodes are added to the society graph, we can reformulate our result as our second hypothesis.

Marriages created in societies with online dating should have a lower divorce rate. Finally, our last welfare measure, size, keeps constant for most of our simulations, so we do not discuss it further.

The detailed data behind Figures 7 b and 9 appear in Appendix A. Our analysis of the expected changes in welfare gives us with two testable hypotheses. In the next Section, we contrast them against data on of interracial marriage in the U.

S, and the quality of the marriages created through online dating. What does the data reveal? Is our model consistent with observed demographic trends? Figure 10 presents the evolution of interracial marriages among newlyweds in the U.

from to , based on the American Community Survey and , and decennial censuses IPUMS. In this Figure, interracial marriages include those between White, Black, Hispanic, Asian, American Indian or multiracial persons.

Data prior to are estimates. The methodology on how the data was collected is described in Livingston and Brown Source: Pew Research Center analysis of American Community Survey and , and decennial censuses IPUMS.

The red, green, and purple lines represent the creation of Match. com, OKCupid, and Tinder, three of the largest dating websites. The blue line represents a linear prediction for — using the data from to We observe that the number of interracial marriages has consistently increased in the last 50 years, as it has been documented by several other authors Kalmijn, ; Fryer, ; Furtado, However, it is intriguing that shortly after the introduction of the first dating websites in , like Match.

com, the percentage of new marriages created by interracial couples increased rapidly. The increase becomes steeper around , when online dating became more popular: it is then when well-known platforms such like OKCupid emerged.

After the increase, the proportion of new interracial marriage jumps again in to Again, it is interesting that this increase occurs shortly after the creation of Tinder, considered the most popular online dating app.

Tinder, created in , has approximately 50 million users and produces more than 12 million matches per day. Matches can be thought of newly established edges, in the language of our model. We do not claim that the increase in the share of new marriages that are interracial in the last 20 years is caused by the emergence of online dating alone, but this finding is in line with Hypothesis 1 in our model.

Another cause for the steep increase described could be that the U. population is more interracial now than 20 years ago. The reduction of the percentage of Americans who are White, falling from However, the change in the population composition in the U. S cannot explain the huge increase in intermarriage that we observe.

In Appendix C we show that, even controlling for demographic change, we observe an increase of interracial marriages, although certainly smaller.

A more transparent way to see that the increase in the number of interracial marriages cannot be due to changes in population composition alone is too look at the growth of interracial marriages for Black Americans. However, the fraction of the U. Random marriage accounting for population change would then predict that the rate of interracial marriages remains roughly constant, although in reality it has more than triplicate in the last 35 years.

Cacioppo et al. The findings of Cacioppo and his coauthors show that our model predictions closely match the observed properties of marriages created online, and its strength compared to marriages created on other, more traditional venues. Our model predicts that, on average, marriages created when online dating becomes available last longer than those created in societies without this technology.

Yet, it is silent regarding comparisons between the strength of interracial and intraracial marriages. There is empirical evidence showing that interracial marriages are more likely to end up in divorce Bratter and King, ; Zhang and Van Hook, Our model is also silent on why some intraracial marriages from a particular race last longer than intraracial marriages from another race e.

Stevenson and Wolfers, show that Blacks who divorce spend more time in their marriage than their White counterparts. The theoretical model we present discusses a general matching problem under network constraints, and hence it can be useful to study other social phenomena besides interracial marriage. The races or communities in our model can be understood as arbitrary groups of highly clustered agents.

Agents can be clustered by race, but also by ethnicity, education, socioeconomic status, religion, nationality, etcetera.

Thus, our theoretical model can be also applied to study interfaith marriages, or marriages between people of different social status. The role of connecting highly clustered groups is also not only linked to online dating. Interestingly, Parey and Waldinger find that participating in ERASMUS to study abroad increases the probability of working abroad by 15 percentage points.

The matching of agents also goes beyond marriage. Think of nodes being researchers at a University, races being academic departments, and edges representing who knows whom.

Matchings indicate academic collaboration in articles or grants. The Euclidean distance interpretation makes sense, as a microeconomist in a business school may be better off partnering with a game theorist at the biology department rather than with an econometrician in his own business school.

Diversity in a University would be then a measure for interdisciplinary research, often encouraged by higher education institutions and funding bodies. Interdiscplinary seminars, for example, could take the role of creating links between academics in different departments.

It would be interesting to test our model against in this other scenarios. We leave this task for further research. We introduce a simple theoretical model which tries to explain the complex process of deciding whom to marry in the times of online dating.

As any model, ours has limitations. Furthermore, it fails to capture many of the complex features of romance in social networks, like love. There are multiple ways to enrich and complicate the model with more parameters. However, the simplicity of our model is its main strength. With a basic structure, it can generate very strong predictions. It suggests that the diversity of societies, measured by the number of interracial marriages in it, should increase drastically after the introduction of online dating.

Societies where online dating is available should produce marriages that are less likely to break up. Both predictions are consistent with observed demographic trends. Simple models are great tools to convey an idea. It could have been enhanced by introducing thousands of parameters. Yet it has broadened the way how we understand racial segregation, and has been widely influential: according to Google Scholar, it has been quoted 3, times by articles coming from sociology to mathematics.

It has provided us a way to think about an ubiquitous phenomenon. In this Appendix we conduct several robustness checks to show that the fast increase in the diversity of societies, described in Result 1 , occurs for many combinations of model parameters. The first exercise we conduct is to simulate the model again, but varying the probability of intraracial connections p to 0. With respect to diversity, long marriages always lead to an almost immediate increase to 1, meaning complete social integration.

This increase is shown in Figure As expected, a society integrates faster when the value of p is higher. With respect to strength, we also observe minor variations, which appear in Figure A smaller p makes agents less connected to potential partners, and thus the strength of resulting marriages becomes weaker.

With long marriages, strength converges very quickly to its optimal value, around 0. The detailed results of our simulations with p equal to 0. The second robustness test we perform is to vary p and q simultaneously but keeping its ratio fixed. Both parameters indicate how connected a person is to people of his own race and to people of other races. To find a good estimate of the ratio p q , we use data from the American Values Survey by the Public Religion Research Institute PRRI , a nonpartisan, independent research organization.

The PRRI data shows that, if a White American has friends, 91 are expected to be of his own race, and 1 Black, 1 Latino, and 1 Asian the rest are multiracial or of unknown race. Black Americans are more interracially connected, with 83 friends expected to be of his own race, 8 Whites, 2 Latinos, and and no Asians. This ratio implies that a person is 10 times more likely to be connected to a person from her own race.

We vary p from 0 to 1. We present the results for Euclidean societies only as we have seen that Euclidean and assortative societies produce almost identical results. A first conclusion we obtain is that, with long marriages, we observe complete integration, just as we did when increasing q alone.

However, this time it does not happen as quickly as when we increase only q. With direct marriages the increase is very fast but full integration is not obtained. But this this conclusion is flawed, because we compare our diversity measure to one where agents were completely connected within their own race, i.

a complete graph. This is a very high percentage of interracial marriages, because we fix that agents are 10 times more connected withing their own race. Finally, the strength levels we observe with direct marriages are the lowest we have found so far, which is not surprising given the small number of potential partners that agents have.

It is equally expected to observe that the strength of a society increases when p grows. The third robustness test we perform is to introduce intraracial preferences, as described in equation 3. We do this in the following intuitive way. Agents prefer marrying someone from their own race β times as much as marrying someone from another race.

We still impose that marrying any potential partner is better than remaining alone for all agents. There is evidence suggesting that persons substitute similarities in race for similarities in personality traits. We used to marry people to which we were somehow connected to: friends of friends, schoolmates, neighbors. Since we were more connected to people similar to us, we were likely to marry someone from our own race. However, online dating has changed this pattern: people who meet online tend to be complete strangers.

Given that one-third of modern marriages start online, the authors investigate theoretically, using random graphs and matching theory, the effects of those previously absent ties in the diversity of modern societies.

The authors find that when a society benefits from previously absent ties, social integration occurs rapidly, even if the number of partners met online is small. Their findings are consistent with the sharp increase in interracial marriages in the U.

Networks in the News. We used to marry people to which we were somehow connected to: friends of friends, schoolmates, neighbors. Since we were more connected to people similar to us, we were likely to marry someone from our own race. However, online dating has changed this pattern: people who meet online tend to be complete strangers.

Given that one-third of modern marriages start online, the authors investigate theoretically, using random graphs and matching theory, the effects of those previously absent ties in the diversity of modern societies. The authors find that when a society benefits from previously absent ties, social integration occurs rapidly, even if the number of partners met online is small.

Their findings are consistent with the sharp increase in interracial marriages in the U. in the last two decades. Read the full article here. by Josué Ortega and Philipp Hergovich We used to marry people to which we were somehow connected to: friends of friends, schoolmates, neighbors. Previous Post Next Post. You may also like Close Menu.

The Strength of Absent Ties: Social Integration via Online Dating Josu e Ortega and Philipp Hergovich October 2, Abstract We used to marry people to which we were somehow · The Strength of Absent Ties: Social Integration via Online Dating. We used to marry people to which we were somehow connected to: friends of friends, schoolmates, We find that when a society benefits from previously absent ties, social integration occurs rapidly, even if the number of partners met online is small. Our findings are consistent with the sharp The Strength of Absent Ties: Social Integration via Online Dating By Philipp Hergovich and Josu e Ortega y First version: September 29, Revised: September 14, We used to We used to marry people to which we were somehow connected to: friends of friends, schoolmates, neighbours. Since we were more connected to people similar to us, we were ... read more

Note that diversity may be above 1. Interestingly, most of this effect is due to the valuable social networks that immigrants gain by marrying a local and not because an easier chance to get a visa. in the last two decades. Result 2. We model online dating in a society S by increasing the number of interracial edges. The main complication of estimating the adjusted rate of interracial marriage is that there is little data available regarding newlyweds. data, and find that, as predicted by our model, the number of interracial marriages substantially increases after the popularization of online dating.

This is 5. population would have remained constant since Our findings are consistent with the sharp increase in interracial marriages in the U. We vary p from 0 to 1. We present our model in Section 2. We do not claim that the increase in the share of new marriages that are interracial in the last 20 years is caused by the emergence of online dating alone, but this finding is in line with Hypothesis 1 in our model. With respect to diversity, long marriages always lead to an almost immediate increase to 1, meaning complete social integration.