The Trojan Horse Effect – On Allocating Funding Only to Democratic Parties (Column 11)

With God’s help

It was reported in the news that the government is considering an additional budget allocation for democratic parties (those that hold primaries) that would not be given to dictatorial parties (those whose representatives are chosen by a selection committee or by the party leader). See here. At first glance this is outrageous, since the large parties are joining forces here and making common cause in order to receive more funding at the expense of the other parties. Beyond that, the primary system is itself disputed, and it is far from clear that this is indeed the best and most democratic method (many argue that it repels good candidates who are unwilling to go around shaking hands at the bar mitzvahs of complete strangers, that it requires considerable money in order to be elected, and that it leads to corruption and outside influence on government—the nexus of wealth and power, and more). The law does not require a party to hold primaries, and therefore a budget allocation that discriminates against such parties seems, at first glance, unjustified. In today’s column I would like to explain why this is a necessary and sensible step, even if not an optimal one.[1]

On the Trojan Horse

The Odyssey tells of a brilliant stratagem by Odysseus through which the fortified city of Troy was conquered. The Greeks, who had laid siege to the city and failed to capture it, hid an entire unit of soldiers inside a large wooden horse that was placed at the foot of the walls of besieged Troy, and then ostensibly lifted the siege and sailed away. The Trojans understood that they had won the campaign, came out beyond the walls with cries of victory, and brought the spoil-horse into the city. The rest is history (or rather mythology). Ever since, down to our own day, the expression ‘Trojan horse’ has been used to describe a foreign element, actually belonging to the rival, that is located within our own camp and may thereby bring about our defeat.

The Trojan Horse Effect in Politics

What am I referring to? In the 19th Knesset there was a party created by the merger of two Religious Zionist parties with a similar ideology: Jewish Home (formerly the National Religious Party) and Tkuma. Tkuma is a nondemocratic religious right-wing party whose Knesset members and platform are determined by a committee of rabbis.[2] Jewish Home is a more liberal religious right-wing party that chooses its representatives through broad primaries and according to a democratic constitution. During that term it became clear that within the Jewish Home faction there were several MKs whose views were completely identical to those of Tkuma (for example, Moti Yogev and Yoni Chetboun). In 2014, MK Moti Yogev of Jewish Home circulated a letter online in which he warned of flaws in the proposed constitution for Jewish Home (which shortly afterward was adopted by a large majority). Among other things, he spoke about the importance of integrating Tkuma’s Knesset members and about the importance of democracy within the party (as against the dictatorship that party chairman Naftali Bennett was allegedly trying to introduce through the proposed constitution).

I could not restrain myself, and in a reply letter I pointed out to him that Tkuma’s representatives are determined by a committee of rabbis, and therefore it is not exactly a democratic model. I drew his attention to the fact that there was a contradiction of sorts in what he was saying. In the course of the correspondence I further argued that he and his like-minded colleagues constituted a Trojan horse within Jewish Home. They are far closer in their views to Tkuma and its rabbis than to Jewish Home, under whose banner they ran for the Knesset. On almost every issue about which there is disagreement between the parties (and in my opinion these are a very large majority of the relevant issues currently on the table), he and his colleagues hold Tkuma’s views. ‘So what are you doing in Jewish Home?’ I asked. ‘Why are you not running under Tkuma’s banner?’

My letter was published and aroused some rather amusing echoes, which I will not enter into here. I received quite a few responses to it (including from Moti Yogev himself). Among other things, it was argued against me that those representatives (Yogev and Chetboun) were democratically elected by the members of the party center, and that they serve as their mouthpiece. It was argued that by what I said I was in effect trying to impose my own positions and outlook on the Jewish Home party, which is composed of various shades. Since these members too are one of the shades among Jewish Home voters, there is no room here to speak of a Trojan horse. Many readers will no doubt identify with these claims, but they involve a simple mathematical misunderstanding. This misunderstanding has ethical and political consequences that touch many areas of our lives, and particularly the confrontation between democracy and fundamentalism. I will therefore try here to clarify my point.

I should note in advance that in the past there was a similar phenomenon in the Likud party as well, which to this day is the main right-wing party in Israel. Within it there was a faction led by MK Moshe Feiglin, a religious man with right-wing and religious worldviews, regarded by many as an alien element and an extremist trying to take over Likud. People protest that he is not acting fairly by running within Likud rather than within Jewish Home or Tkuma, or by forming a party of his own (which is what he has been doing recently, after Likud did not choose him for the current Knesset). Feiglin and his people respond that they are legitimate Likud people and that their representatives are duly elected within the party’s primaries; flesh of Likud’s flesh. On the face of it, those who protest against them want to impose their own positions on the whole party, exactly as in my case with Jewish Home described above. I am not among Feiglin’s supporters (though I do appreciate him and his views and arguments), and I am not even sure that he acts wisely on the political plane. But I never understood what was ethically illegitimate about what he was doing. Democratic elections were held—primaries, a party center, and the other democratic institutions—and whoever is chosen is the one who best represents the voters. But after the correspondence with Moti Yogev, the penny finally dropped for me. The same ethical-mathematical mistake is involved here.

To understand this, let us return to Jewish Home. As noted, Tkuma’s MKs and voting profile are determined by the rabbis’ committee, without any influence from voters—no center, no primaries, and the like—and therefore there is no point in joining that party, since in any event the rank-and-file member has no ability to exert influence. What is the perplexed member to do if he nonetheless wants to try to have some influence? Very simple: he joins Jewish Home. There he can have influence. He will choose the Knesset representatives and influence the party’s course. And indeed, many voters with distinctly Tkuma views join the Jewish Home center en masse, and even succeed in placing their representatives as MKs on behalf of Jewish Home. What now happens? Jewish Home’s representatives are composed of some whose outlook is that of Jewish Home alongside others whose outlook is that of Tkuma (and who were indeed duly elected). In addition, of course, places are reserved on the combined party list for representatives of Tkuma itself (who were chosen by the rabbis’ committee). What do we get? Tkuma’s path wins double influence: it has substantial representation among Jewish Home’s Knesset members, and in addition the list also contains Tkuma’s own Knesset members.

Let us think about how the proportions on such a Knesset list are determined in a merger of this sort (the proper combination). General polls examine Tkuma’s electoral strength relative to Jewish Home and reveal that it is worth several mandates (say four, purely for the sake of discussion). Why? Because in such a questionnaire, just as in elections to the Knesset (had the parties run separately), all Jewish Home voters who hold those views would in any event vote for Tkuma, and therefore they report positions like hers. The meaning is that the electoral strength of Tkuma’s outlook is built partly on Jewish Home voters as well. Tkuma now demands proper integration, that is, representation proportional to its electorate, which as noted stands at four mandates. A most justified demand, no? In the end it receives representation on the joint Knesset list that is based both on representatives elected by Jewish Home party members and on members who come directly on its behalf. Thus we get an upgraded level of representation for it in the Knesset, while at the same time, of course, the democratic party alongside it is under-represented.

Let us make a simple calculation and see clearly what we have here. Suppose that the Religious Zionist public, together with the secular voters who vote for Jewish Home-Tkuma, constitutes a certain segment of the Israeli population, say one million voters in all. That million is divided into two components, which we shall call X (those with the outlook of Jewish Home) and Y (those with the outlook of Tkuma). For the sake of discussion, let us further assume that X has an electorate of about 70% of the total million. X is a democratic party whose representatives are chosen in primaries and which is run by a party center. By contrast, Y, which enjoys support from 30% of that million, is a party whose representatives and course are determined by a central committee of unelected figures (rabbis, or a selection committee) without primaries. Now, dear reader, go and calculate how many representatives the Y outlook will have in the Knesset.

Answer: if we assume that the combined party has 20 MKs, then of these, 6 will be reserved for people with the Y outlook (in accordance with their rate of support in the population—the proper combination). But among the other 14 there will be another 30% with the Y outlook, since 30% of Jewish Home’s party members actually hold Tkuma’s outlook. In other words, more than 4 MKs are added here to the original 6. Altogether Y will have more than 10 MKs, that is, more than half the MKs on the combined list, even though its true rate of support among the voters is, as noted, only 30%. That is the entire theory of the Trojan horse. This is how a nondemocratic party upgrades its strength in the Knesset at the expense of its sister democratic party.

So What’s the Problem?

If we return to our specific case, Yoni Chetboun and Moti Yogev are those additional MKs who represent Tkuma within Jewish Home without justification, and therefore I argued that they are a Trojan horse and that their conduct is unethical. Since I believe they are decent people, I conclude that this is a consequence of a mathematical misunderstanding. By now any child can understand that the claims that they were democratically elected and therefore represent Jewish Home voters stem from a purely mathematical mistake. The Trojan horse effect leads to an unfair upgrading of the power of a minority and to the under-representation of the democratic party. In essence, this is a maneuver—not contrary to the law—used by the losing minority in order to defeat the majority and become a majority.

In war, such a maneuver is certainly legitimate (as far as I recall, a Trojan horse does not violate the Geneva Convention; Odysseus would not stand trial before the international court in The Hague). After all, if ambush or killing is permitted in order to win a war, then surely deception and such tricks are permitted as well. But in politics that purports to be fair, this is entirely illegitimate. In fair politics, the main goal is that representatives should faithfully reflect the distribution of opinions within the public, so that decisions will be made that reflect what the public wants. There is no doubt that this is not what is happening here.

A First Solution

Let us now take an up-to-date time-out. Naftali Bennett, chairman of the Jewish Home party, inserted into that constitution a clause that allows him to place one candidate of his own in every block of five candidates for the Knesset. This was one of the main clauses that aroused the anger of the opponents of the proposed constitution (there is no need to mention who they were: Yogev and Chetboun). Let us do the math now: we saw that out of 20 MKs, 10 represent Tkuma instead of 6. One in every block of five will remove 4 representatives here and insert in their place representatives whose outlook is that of Jewish Home itself. And lo and behold, we have arrived exactly back at fair representation. It is striking to me that it is precisely the Tkuma people within Jewish Home, who created the distortion, who are exactly the ones protesting against the constitution that corrects it. The contradiction I spoke about in Yogev’s words receives mathematical confirmation here. This is precisely the meaning of the proposal I mentioned at the beginning of these remarks: to increase funding for democratic parties at the expense of the dictatorial ones.

Does the Effect Exist Only When There Is a Combination?

Let us now continue analyzing the Trojan horse effect itself. There is another important point worth noting: this phenomenon occurs only because of a combination of a democratic party with one that is not such. This rests on the following proposition (we are back to mathematics): in combinations of two nondemocratic parties, or of two democratic parties, this effect does not exist. When both parties are democratic, then just as one can insert Trojan horses from party X into party Y, one can also do the reverse; that preserves symmetry and representativeness. In such a situation, the ability to perform maneuvers is available to both sides, and in practice there is no motivation to do so (a person wants and is able to exert influence in his own party and not in another). It should be remembered that beyond the effect of symmetry, under current law one cannot join two different parties. Therefore it is unlikely that a person will go to a party that does not suit him, for by doing so he loses the possibility of influencing his own party. Even if both parties are nondemocratic, again there is no problem, since in that case there are no primaries and the Trojan horses have no city to enter. But when one party is democratic and the other is not democratic, then and only then are distortion and asymmetry created. In such a situation there will arise the phenomenon of people joining a party for which they do not vote in the election, and thus a bias in representativeness is created.

If we continue with the mathematics, it would seem at first glance that what we have here is a problematic application of game theory. In its early stages, game theory dealt with strategic comparisons of individual players in order to arrive optimally at victory over their rivals. Later studies, however, showed that we must also take into account the possibility of forming coalitions. Sometimes a coalition will give its partners a better result against their rivals than each would get by playing alone. At first glance, that is exactly what is happening here. Tkuma’s coalition with Jewish Home gives Tkuma a better result than running separately. The big question, of course, is what the Jewish Home party gains from this coalition. A coalition ought to arise only if it brings benefit to both sides (in the terminology of game theory, a strong Pareto improvement), or if some gain and the others at least do not lose (a weak Pareto improvement), but certainly not when one side gains at the expense of another side that is harmed. One can discuss the benefit that a large list brings simply by virtue of its size, but we shall soon see that all of this is irrelevant.

The perceptive reader will surely notice that in fact all this is a mistake. The Trojan horse effect is created by the very existence of nondemocratic parties in the political arena, entirely irrespective of the question whether they are combined with other parties in running for the Knesset. We can see this again through the example that has been accompanying us. Had Tkuma run separately, it is easy to see that the problem would still remain. Its voters could still join Jewish Home and choose its representatives, and they would probably do so (in order to exert influence), while at the same time voting for Tkuma at the ballot box. In this way Tkuma would achieve upgraded influence in the Knesset according to exactly the same formula. The combination of the parties is not a condition for the existence of the Trojan horse effect.[3]

It is worth noting the following nontrivial implication: in the United States, which is a two-party country (Democrats and Republicans), if one of the two parties had a support rate of 30%, that would apparently be very discouraging from its perspective. But do not despair: such a party has a sure way to take over the leadership of the state. It must cancel its primaries and become nondemocratic, and then send its supporters to vote in the rival party’s primaries (they would probably go there even without being sent). That is all. Alternatively, here in Israel too, if there is a single nondemocratic party in the Knesset whose rate of support in the general population is 30% (Arabs, Haredim, kibbutzniks, redheads, or any other sector), it can employ the Trojan horse maneuver and receive the leadership of the state by an absolute majority (without a coalition) on a silver platter.

Feiglin’s Mistake and Moti Yogev’s

Now let me pause once more to explain why Feiglin’s mistake was smaller than that of Yogev and Chetboun. There are two reasons for this: a. Feiglin’s people in Likud have no nondemocratic option for which they can vote despite having joined Likud, except for Tkuma. In other words, most of them really do also vote for Likud at the ballot box, and therefore the effect of under-representation does not exist, or is very small. Moreover, the relevant option for them is Jewish Home, which is also a democratic party, and as stated, in a democracy-democracy situation there is no problem because of the symmetry assumption. b. Likud presents itself as not a sectoral party but rather a general party of the Israeli right, and that consists of religious and secular people and other shades. Therefore it is precisely there that Feiglin’s people can indeed be considered legitimate Likud voters (provided that they also vote for Likud at the ballot box). But in the case of Jewish Home there are two clear shades, and fairness says that the voters and members of the center should divide between them according to their outlook.

Further Solutions

The obvious conclusion is that even dismantling the coalition between Tkuma and Jewish Home will not help here. So what can be done? One thing that could prevent this problematic effect is the democratization of all the parties in the country. If there were a law requiring all parties running for the Knesset to conduct themselves democratically, the distortions in representation would disappear. Even if it seems problematic to us that the law should dictate to parties how they are to conduct themselves, without it distortions arise that dictate situations of under-representation to other parties. Another possibility is to abolish democracy in all parties (either all are run by a selection committee, or all by a party center). But that too is somewhat troubling, at least to those who believe in the existing system. A third possibility is, of course, to rely on the fairness and basic mathematical competence of the voters of all the nondemocratic parties (that they will not employ the Trojan horse maneuver). I personally would not build on that, and reality proves as much. A law is preferable.

At present the government is proposing a path of increasing funding as an offset to this effect, but even this path does not eliminate the effect. It seems to me that the best way to prevent it is by means of a method suggested by someone I know (to my shame I no longer remember who) who proposed establishing that a person who joined some party and voted in its primaries would no longer be able to vote in the upcoming election. His vote would automatically be counted in favor of the party he joined. It seems to me that this is indeed the best solution. Such a solution renders unnecessary the government’s current proposal, which speaks of corrective budgetary preference.

Quantitative Analysis

I will now present a short and simple quantitative analysis of this phenomenon. Suppose that party Y (the nondemocratic one) has a support rate of P (a fraction between 0 and 1) among all the voters in the sector. As a result of the Trojan horse maneuver it receives representation at the following rate:

Ny(P)=P+P(1-P)=2P-P^2. At both extremes (P=0 and P=1) one gets exactly the proper representative result, but of course these are cases in which the problem does not exist to begin with (either party X does not exist or party Y does not exist; it is not really a situation of two parties). In all other cases the Trojan horse effect works in favor of the nondemocratic party. This means that there is built-in under-representation for the democratic party. The effect is described in the following graph:

P is the true support rate for party Y out of all the voters in the sector. Ny(P) is the number of its representatives who will actually enter, out of all the representatives who will enter on behalf of the sector. The dotted line expresses proper representation (Ny=P), and one immediately sees that it is always below the actual line. That is, essentially and without exception, there is always under-representation of the democratic part of the political map.

When is it most worthwhile for a nondemocratic party Y to employ the Trojan horse maneuver? To answer that, we have to divide the result we obtained by the proper representation, that is, by P itself. What we get is: 2-P. The meaning is that the lower the rate of support for party Y, the more worthwhile it is for it to employ the Trojan horse maneuver, that is, to plant its voters in the centers of other democratic parties. When it has very little support, it can thereby double its power. In other words, the less support you have (or the less you are winning in battle, like Odysseus), the more you gain from the Trojan horse maneuver. And concerning this the Sages said: Be careful with the children of the poor, for Torah will come forth from them. (‘Be careful with the children of the poor, for Torah will come forth from them’).

It is interesting to see the result for the representation of the democratic party X in such a situation. Clearly, this is the complement to 1 of the representation of party Y, namely: Nx(P) = 1 – Ny(P) = 1 – (2P – P^2) = (1 – P)^2. If we remember that 1-P is precisely the public support rate for the democratic party, then the result obtained here is that this party receives representation equal to the square of its true rate of support in the public. The explanation is simple: representation is the percentage of support for it (the percentage of voters who support X in its own primaries, 70% in the previous example), taken from within a representation whose size is itself again the percentage of support for it (that is, from within the number of Knesset members at its disposal, 14 in the previous example). One should remember that this is a fraction, and therefore squaring it always reduces the representation. As stated, if a nondemocratic party exists, then the democratic party is always under-represented in the Knesset. Let us continue with the example that has accompanied us throughout the chapter: if Tkuma’s rate of support out of the voters of Tkuma and Jewish Home together is 30%, then P=0.3, and the rate of support for Jewish Home is 1-P=0.7. One immediately gets that the number of Jewish Home representatives in the Knesset falls below half the Knesset members of the two parties together ((0.7)^2=0.49). The number of Tkuma representatives is of course the complement (0.51), which is above half the Knesset members. Their lack of democracy and their Trojan horse maneuver give them a very handsome bonus in representation.

By the same token, as I also noted above, if there were a nondemocratic party in Israel or in the United States that enjoyed a support rate of 30% in the general population, and if all the other parties conducted themselves democratically, then the Trojan horse maneuver would give the minority party representation of 51% of the members of parliament, that is, exclusive control of the state (without any need for a coalition). Interesting, is it not?

On Fundamentalism

We are now beginning to reach the subject of fundamentalism. The under-representation effect of the Trojan horse can explain several additional things. For example, it can explain the built-in advantage of a fundamentalist society over an open and democratic society (see the introduction to my book Emet Ve-lo Yatziv). Muslims are flooding Europe and participating in the democratic process that takes place there. The infrastructure built by democratic societies now stands available for the use of members with nondemocratic conceptions as well (of course, not all Muslims are such). In this way fundamentalist Islam receives over-representation in international institutions and in world politics (at the UN, in the press, and in international discourse generally). We have states that are themselves fundamentalist, but now even the states that are not such (only the democratic ones among them, of course) partially represent fundamentalist views and interests. There you have, in a nutshell, an explanation (partial and somewhat simplistic, of course) for the standing of Israel and of democracy in the world and at the UN.

Another example is the situation in the negotiations being conducted between Israel and the Palestinians. Palestinian society, even if we assume that it has some measure of democracy, is certainly unwilling to accept Jewish residents into its midst, even those who lawfully purchased their homes, and certainly unwilling to give them political power (think of a Jewish party running in elections to the Palestinian Authority; it sounds absurd and imaginary). That nondemocratic society stands—whether negotiating or, alternatively, fighting—opposite a democratic society (Israeli society), part of which consists of Palestinian Arabs who are citizens of Israel, and who receive influence, civil rights, and representation in the Knesset and in government. Therefore the Israeli position itself is multivocal, meaning that within it too there is partial expression of the Palestinian position. Put more vividly, there are actually Palestinians on both sides of the negotiating table. Now Palestinian citizens of Israel come and argue (in a way that is certainly not detached from the facts) that there is under-representation and inequality in the institutions of Israeli government. Does this remind you of anything?

I should emphasize that precisely here I personally do not support such discrimination on the formal plane, that is, anchoring in legislation that Arabs could not participate in government. I am in favor of democracy and equality for all citizens, and I believe that the character of our state ought to be determined by all citizens and not only by some of them. In other words, it is difficult to accept a demand for democracy among the Palestinians in their authority as a condition for including Israel’s Arabs in the democratic game among us. By the same token, it is not reasonable (nor practical) to demand that they move there and vote there. It is even harder to give up our democracy. Therefore the resemblance to the case of Tkuma and Jewish Home is not perfect. But on the other hand, I am not surprised that in practice Zionist parties and Zionist leaders do not tend to include the Arab parties in the government. Who wants his rivals to conduct negotiations from both sides of the table and make decisions about his own fate?! Troy is here.

I will now continue the analogy and claim that this effect is an expression of democratic failure, that is, of the inability of a pluralistic democracy to defend itself against fundamentalism. At the beginning of my book Emet Ve-lo Yatziv I defined fundamentalism as full trust in a supreme source of information or in a charismatic figure, expressed in the suspension of critical thought. The meaning of this in the political field is the creation of a party led by such figures, so that the ordinary voter sees no importance in exercising his critical thinking or in having influence over the party. Therefore he does not make his support for the party conditional on his ability to influence the choice of representatives and its decision-making. This is exactly the profile of party Y: it has no primaries, and its representatives and course are determined by those possessed of higher knowledge who do not err. For our purposes here, it represents fundamentalism (at least in its philosophical sense). What will its voters do if they wish to gain influence? They will turn to the competing party X, which is democratic, join it, and attach themselves to its center, and thus vote within it in the primaries and determine its representatives; they will also vote in the center and determine its political agenda.

Later in that book I explained the meaning of this in terms of synthetic and analytic thinking, and in terms of tolerance and pluralism that are discussed there. I concluded by saying that the Trojan horse effect is a mathematical expression of that same built-in failure in the confrontation between fundamentalism and an overly democratic pluralism (that is, a postmodern pluralism). I showed there that the only way out is to relinquish substantive pluralism and adopt conceptions that I there called synthetic. I will not go into all of that here.

Summary

In light of what has been described here, it seems to me that there is some logic in adding budget funds to democratic parties, not because primaries are the best method but because they create a built-in disadvantage vis-à-vis dictatorial parties. Still, as I argued above, there are better ways to correct this.

[1] The source of these remarks is an article I wrote on the Trojan horse effect for the now-defunct journal Pasifas.

Afterward I also incorporated these ideas into my book Emet Ve-lo Yatziv (in chapter 26. There the discussion was presented as a certain expression of the inability of democracy to cope with fundamentalism). I will add that I sent the article to several MKs, and perhaps it had some effect on the current step. Or perhaps that is excessive optimism… (Who reads at all?). The present article is based on the chapter in the book, with the necessary omissions and corrections.

[2] It also has a party center, but that too is controlled by those same rabbis, and therefore it is meaningless for our purposes.

[3] The combination of the parties on a single list for the Knesset nevertheless does have some secondary effect, if one takes the electoral threshold into account. If party Y has no possibility of entering the Knesset on its own because its support rate P is below the electoral threshold, then in order to bring in its own representatives it must combine with a larger party. In such a case, the combination gives it a double upgrade: the very entry of its own representatives into the Knesset (at the level of proper representation, P) in addition to the Trojan horse effect (that which exceeds proper representation; see the graph below). Note that the first upgrade is obtained only from combining the lists for the Knesset, but the second, as stated, does not depend at all on such a combination.