Published on 12/07/2012 12:57 British Summer Time

Jeremy Bentham created an algebraic formula demonstrating the sum of utility derived from how national political system is structured. The algebraic formula is as follows:

Increasing the weight on one branch of these three decreases the weight on the other two branches. Bentham argued that the current (Contemporary) British system balances the weights among these three branches at the feasible level to maximise the utility.

Nonetheless, Bentham also insisted on abolition of sovereign = monarchy or dictator when his/her existence starts reducing the sum of utility rather than increasing it, and then the revolution shall be emerged. The coefficients of these variable, their sign (+/-), and their significance vary across different time, place (culture and civilisation), and occasion (GDP growth, etc).

At the contemporary time period when Bentham was alive, there was little objective ways to measure the sum of individuals' happiness in each nation in the world. By contrast, due to the development of the information technology, we have become able to collect some peer assessed numerical indices of various social scientific data sets. This happiness index is also collected by objective view points and survey methods under an academic peer assessment. Thus, it is interesting to assess Benthamite calculus owing to this world happiness index.

The data showing how the political system is structured in each nation in the world is quoted from "The Independent Map of the world in 2005". The binary variables are used as the indices to show how one nation's politics is structured e.g. Absolute Monarchy, One Party system, or Indirect/Direct Democracy. There is only one change from the original Benthamite algebra, which is that Aristocracy implies the executive member of a national legislature. As Bentham mentioned Aristocrats were those who have wisdom to govern, so it is equivalent to the government and bureaucratic elites. (He mentioned the House of Lord whose member is not elected from citizens. So, as the members of the legislature is directly appointed by an authoritarian legislation not by individual citizens) Then, many countries governed by one party technocratic policy is seen to be a pure aristocratic system. Absolute monarchy is assumed not to have any influential technocratic institution i.e. aristocracy. (Saudi Arabia and Morocco) whereas the constitutional monarchist nations have an influential parliament (E.g. Arab Emirates). All indirect democratic countries hold both Aristocracy = Technocratic Legislature and Democracy. They are still democratic but not the pure direct democracy. Only the nation seen to be a pure direct democratic is Switzerland in this analysis. Thus, the binary variable representing Monarchy is zero, the binary variable representing Aristocracy is 1, and the binary variable representing Democracy is 1.

**************** An important note ****************

The binary variables are usually 0 or 1, but there are some exceptions.

-> All the British Commonwealth nations have the binary variable denoting "Monarchy" that is 0.3 instead of either 0 or 1. These nations technically have a monarchy but s/he is not their own monarchy living in their countries, and his/her influence is not that strong as much as those nations having their own monarchy like Britain and Japan.

-> The "transient" democratic nations have the binary variable denoting "Democracy" that is 0.5 instead of either 0 or 1. It is still democratic but not a stable democracy. So, the effect of the variable "Democracy" is considered to be marginal.

**************** ***************** ****************

In addition, the Happy Planet Index (HPI) used as the dependent variable in this regression analysis is highly affected by the "natural climate" in these nations. Some nations in a certain latitude mark a significantly higher HPI than the others. Therefore, the absolute value of nation's latitude and its squared value, as the exogenous explanatory variables, are regressed on the HPI as same as the previously mentioned binary variables. The reason why the binomial function of Latitude, instead of a single variable (The linear function), is to demonstrate the parabolic function. The linear model (Regressing only on |Latitude|) only express either the right middle of equator or the North pole and the South pole are the happiest place to live. But, the HPI certainly shows that the optimum latitude to maximise the happiness is somewhere not far away from equator but not the zero latitude point.

All in all, the formula for the regression analysis is as follows:

*** The dependent variable is the natural log of the Happiness Planet Index (HPI) ***

The binomial function showing the climate effect (Latitude) is "the absolute value of Latitude + The squared value of Latitude".

In addition, there are the three binary variables. There are three binary variables showing the pure effect. The first one describes the pure effect of Monarchy. The second one describes the pure effect of Aristocracy. Then, the third one describes the pure effect of democracy.

The rest of variables are the binary variable denoting the interactive effect by two or three variables together. The interaction effect by "Monarchy" and "Democracy" is not assessed because there is no country having both monarchy and democracy without an aristocracy=technocratic executive branch.

The coefficients and their significance is as follows:

The coefficients of the variables showing the climate effect are 0.02256 for the coefficient of the absolute value of Latitude and -0.0004 for the squared variable of the latitude. Then, the formula shapes an upward parabola shown in the picture below.

Therefore, the place where the latitude is either +31 or -31 maximises the happiness of people living.

All the three binary variables denoting the single effect have a significant and positive coefficient. Both the interaction of Monarchy and Aristocracy and the interaction of Aristocracy and Democracy have a significant and negative coefficient. The coefficient of the interaction of all three variables is non-significant, so that the half of the coefficient value is used. The HPI derived from each different political structure is as follows:

This is a bar graph showing the policy effect on the H.P.I.:

These trends can be roughly visualised in a picture graph like this:

A nation with the direct democracy (Monarchy = 0, Aristocracy = 0, Democracy = 1 ) produces the highest HIP. But, Switzerland is the only nation with such a system in the world. So, it is not sure if it is still significant number of the sample to prove its superiority.

The absolute monarchist nations, (Monarchy = 1, Aristocracy = 0, Democracy = 0 ) is the second best. But, there are only Saudi Arabia and Morocco as the examples. Furthermore, all the other monarchist nations without any democratic structure (Monarchy = 1, Aristocracy = 1, Democracy = 0 ) showed the lowest HPI. Thus, it can be seen that, in general, monarchism without any degree of democracy is more likely to cause unhappiness rather than happiness.

The nations with one party system mark the second lowest HPI. Even though these nations are more efficient to be stablised than those lowest developed nations, the transient democratic nations, and any non-democratic monarchist nations. Nonetheless, they seem to sacrifice happiness for their stability.

Some of the constitutional monarchist nations with democracy seem to be happier than democratic republic nations. But, majority of the constitutional monarchist nations are less happier than democratic republic nations.

The democratic republic nations, though their democracy is indirect, such as the United States of America and France are the happiest nations next to Switzerland, the direct democratic nation.

All in all, Democratic Republican nations at the latitude of 31 or -31 seem to be the happiest ones. It also looks like that we can try to establish another Direct Democratic country because it looks like maxminising the happiness of individuals in a nation. Nonetheless, only the sample is Switzerland and it is never known if the similar model is applicable to increase the happiness in another country in reality. The democratic republic nations perform well among all. The performance of the constitutional monarchist nations with an indirect democracy varies.

Hence, this econometric analysis seems to be able to assist Jeremy Bentham having argued that, if monarchy start causing disutility rather than utility, then it is time for revolution! Perhaps, we have never known that there will be a revolution for the cause of Direct Democracy, the unknown ideal, in the near future? The Direct Democracy seems to maximise individuals' happiness at the optimum level (Though there is not enough number of the sample to prove in reality) by means of this statistic inference.

* It was difficult to find if the model creates heteroscedasticity: Some tests said no, but the other said yes. But, this analysis was mainly composed of the binary variables, and the dependent variable used in this analysis is not a precisely scientifically accurate variable. So, the aim of test should not be strict as much as the other econometric analyses.

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