# A Numeric Multi-Status Demographic Model of a Jewish diaspora

Леонид Александрович Ашкинази

A Numeric Multi-Status Demographic Model of a Jewish diaspora


A numeric model of a national group has been developed. (In this work, the term "national" is used in the sense close to "ethnical," rather than "belonging to or maintained by the federal government.") The model describes a national group as consisting of a set of categories. The model has been used to explore a Jewish diaspora. The American Jewish Diaspora was studied in most detail since these diasporas exists in a stable political situation, in which case a demographic forecast is most reliable.


In the model, each category represents people with a particular national behavior. People belonging to different categories differ in their marriage preferences, birth rate, and their attitude to bringing up children. For example, people from one category may admit only marriages with people from the same category. People from another category may admit marriages with people from other categories, but within the same national group. People from a third category may admit marriages with people from other national groups. In some categories, people do not permit birth rate control, in others they do. In some categories, national bringing up of children is obligatory, in others it is not. (By "national bringing up" we mean acquainting children with national culture, traditions, and cultural wealth that would create strong national self-identification.) An example of the described segmenting of a national group is a Jewish Diaspora.


According to the model, the evolution of a national group (whose representatives may live in different countries) and its categories depends on characteristics mentioned above, though in the real life national behavior of people is mainly based on self-identification and reaction of people from other national groups.


It is clear that any model provides reliable results only if source data are authentic. However, a model can be used to determine what parameters affect the results most of all. Knowing this, it is possible to direct efforts to defining the values for the most affecting parameters. It may happen that these values are known.


There is a common opinion that survival of a national group is promoted by limitation of mixed marriages, high birth rate, and national bringing up of children. For a national group consisting of one category, the proportion of parameter values that provide the group survival can be obtained analytically. However, a multi-category group can be studied only using a numeric model.


We have developed and explored a model that divides a national group into four categories. In the model, national behavior of people depends on the following parameter types:

-- Birth rate;

-- Internal marriage preference index (probability of marriage with people from different category within the national group);

-- External marriage preference index (probability of marriage with people from other national groups);

-- National bringing-up index (probability of falling children into a particular category within the group or to another national group).


Assuming that the parameters are sorted by "strength" (different sort criteria may be applied), we can distinguish the following categories within a national group: people that have all four properties (the most "national"); people that have three properties; etc. The model can be easily extended to include a greater number of parameters. Also, the model can be used for a group with lesser number of components without any modifications by proper choice of initial counts and/or parameter values.


Modeling is performed in a step-wise fashion. Each step imitates change of a generation. It involves formation of marital pairs, birth of children, and national identification of children (what category the children will belong to). In the next step, the children (i.e. new generation) form marital pairs. Our primary goal was to determine how existence of multiple categories, mixed marriages, and national identification of children affect evolution of a national group. Since some parameters representing these properties are defined without proper precision, there is no sense in increasing precision in other areas, e.g. increasing granularity of a step.


Marriages are modeled in the following manner. The female population of each category is divided into sub-categories. The number of sub-categories is equal to the number of categories plus one. Each sub-category represents potential marital partners from the current category for male population of one of categories (including the same category). One sub-category represents potential partners for male population outside the national group. The size of each sub-category is proportional to the corresponding female marriage preference index multiplied by the male population of the corresponding sub-category (or outside the group). Then the male population of each category is divided into sub-categories in the same manner. We assumed that female and male marriage preference indexes are equal. After that, for each pair of categories, marital pairs are formed. The number of pairs is the minimum from the sizes of corresponding female and male sub-categories. Once the pairs are formed, the procedure is repeated for the remaining population. The formation of marital pairs is proceeded until any of the following criteria is met: the percentage of not married population is lesser than a threshold value, or the percentage of pairs formed in the current step is lesser than the other threshold value. Both threshold values may be tuned.


All the parameter values (marriage preference indexes, birth rate, and national bringing-up index) are invariable and do not depend on time (represented as number of step). Emigration is not accounted. Dependence of parameters on time and/or immigration can be introduced into the model easily. However, there is no reason in introducing them.


Varying parameter values, it is possible to simulate different situations. If the borders between categories are strict (marriages take place only within the same category), the results are trivial. Categories with high birth rate exist independently, categories with low birth rate disappear, and categories whose representatives admit mix marriages with people from other national groups may maintain their amounts by national bringing up of children born in mixed marriages. In the real life, borders between categories are not strict. In a realistic variant of parameter values, the "rules of behavior" are set so that the more behavior deviates from a rigid one, the less is probability of the deviation.


The model was explored using an example of the Jewish Diaspora. Parameter values for marriage preference indexes, birth rate, and national bringing up indexes were obtained from the literature or by expert estimations. A category that a child gets into was defined from her/his parent categories. Also, a child can get into a different category with probability decreasing with increase of the distance from the parent categories. Marriage preference indexes depend on distances between potential partners' categories: the more is the distance, the less is the index value.


We have explored four variants of the model.


The first model describes the Russian Jewish Diaspora. In this variant of the model, the category names are "Orthodoxes," "Reformists," "Non-Observing," and "Assimilants". Orthodoxes marry only Orthodoxes, have high birth rate and high national bringing-up index. Reformists differ from them in having lower birth rate. Non-observing permit marriages outside their category but within the national group and have high national bringing-up index. Assimilants permit marriages outside the national group, but have high national bringing-up index.


The second model describes the American Jewish Diaspora, the category names are "Orthodoxes," "Conservators", "Reformists," and "Non-religious".


The third model describes a Diaspora in which there is only one category. The population is distributed according to the Jewish tradition: people are classified as "Jews" and "Non-Jews," and the nationality of a child is inherited from mother.


The fourth model describes a Diaspora in which distribution between categories is governed by "ethnographical" rules: population consists of "Full Jews," "Half-Jews," "Quarter-Jews," and "Non-Jews". Categories that children get into are defined as follows. A child of a Full Jew and a Half-Jew becomes a Full Jew or a Half-Jew with equal probabilities. A child of a Half-Jew and a Quarter-Jew becomes a Half-Jew or a Quarter-Jew with equal probabilities, and so on. These rules are defined in order to better approximate the real life without introducing additional categories.


The latter two variants of the model are out of the scope of our approach. They were suggested by some colleagues during a discussion of our work. We have considered these variants just to demonstrate universality of our algorithms.


For the Russian Jewish Diaspora, the modeling results show that in a wide range of parameter values, the major sources of the Diaspora supply are: Jewish bringing-up of children from mixed marriages (i.e. marriages with representatives of other national groups), and higher birth rate for marriages within the Non-Observing category and marriages of the Non-Observing with Reformists. Thus, for this variant of the model, the most important parameters for a demographic prediction are: birth rate for marriages within Non-Observing category and marriages of Non-Observing with Reformists, as well as national bringing-up indexes for mixed marriages.


If the birth rate is 1.3, the total amount of the Russian Diaspora decreases 7 times from the first to the fourth generation and then decreases 30 times from the fourth to the tenth generation. If the birth rate is 1.7, the decrease rates are 6 times and 11 times respectively. If the birth rate is 2.5, they are 4 times and 2 times respectively. Distribution of children between categories and marriage preferences faintly affect the total group amount. If the birth rate is 1.7 and the share of children from mixed marriages who become Jewish is 100%, the total amount of the Russian Diaspora decreases 4 times from the first generation to the third one and then decreases 2 times from the fourth generation to the tenth one. In terms of the model, it means that the children from mixed marriages should become Assimilants rather than Non-Observing in order to marry people from other national groups and bring up their children so that they become Jewish.


For the American Diaspora, the initial group sizes, marital preferences and the proportion of children in mixed marriages who returns to the community were chosen to coincide with all the characteristics known from the literature. Initial group sizes for Orthodoxes, Conservators, Reformists and Non-religious were set in proportion 30-100-75-95 (total 300). Hereinafter all the numbers are the group sizes of people of the same sex in tens of thousands. It is important to note that the absolute group sizes are not important for the calculations and here they are presented for illustrative purposes. Marriage preferences were set so that the proportion of mixed marriages in the whole group was 45%. The distribution of children by category was set so that the proportion of children from mixed marriages who returns to the community was 25%. Under these conditions, the number of all the four categories in the fourth and tenth generations will, respectively, be 34-55-41-41 (total 171) and 37-25-21-13 (total 96). We can observe the decrease of total group size (which later will be replaced by the slow growth) and increase of the proportion of Orthodoxes from 10% to 20% in the fourth and 40% in the tenth generation -- the growth, which is already being noted in America.

As it is accepted when dealing with such models, further we examined the sensitivity of situation to variation of the parameters. It turned out that the variation of the birth rate by 10% -- from 4 to 4.5 children per family -- in purely Orthodox marriages changes the situation as follows: the fourth generation is 40-60-44-42 (total 186), the tenth generation is 82-51-44-27 (total 204).

With the increase of the birth rate to 4.8, the number of diaspora population recovers by the tenth generation, and with the increase to 7.5 the number of diaspora population recovers by the fourth generation (with an intermediate 10% decline).

Change of the birth rate from 1.5 to 1.7 for all other types of marriages does not affect the situation much. Change of marriage preferences -- the decrease of the proportion of mixed marriages by 10% -- does not significantly affect the size of the community.

The influence of distribution of children by categories turned out to be much more complex. In terms of increasing the number of community, the effect depends on the group, from which we take these, for example, 10% of all children, and to which one we transfer them (i.e. from those children who come to Jewish schools and who come out of them). For example, for the American Diaspora the strongest effect takes place if we reduce the number of Non-religious and increase the number of Orthodoxes among the children from Orthodox marriages (or provide the shift of 10% of the total number of children in each group to the next group). In this case, group sizes of the fourth-tenth generations are 180-260 tens of thousands of people. The effect from the shift to the Orthodoxy of 10% of children of mixed marriages turned out to be the second strongest one. In this case, the number of the fourth-tenth generations are 180-124 tens of thousands of people. Thus, the long-lasting effect of shift of 10% of all children to Orthodoxy may be greater than the effect of increase of the birth rate from 4 to 4.5.

Thus, it can be concluded that for the maintaining of the size of the American Diaspora community at this stage the most significant factor is the birth rate in Orthodox marriages and the creation of system of schools, whose graduates will fill up the group of Orthodoxes or the group which is now called "modern Orthodoxes" in America (with the birth rate at the level of 4).

Ashkinazi L.A., Gainer M.L.