Different political styles, views, and beliefs could be considered different strategies or algorithms to solve problems.
So-called "right-wing" beliefs may include the following features:
1) strict rules
2) a clearly polarized distinction between "right" and "wrong"
3) perhaps an emphasis on facilitating the progress of the most "elite" members of the group (whether this be in an economic sense, or in terms of other types of accomplishment). The thinking could be that if the "elite" are flourishing, then the entire society will ultimately flourish, either through a "trickle-down" effect, or through a type of "natural selection" process.
Disadvantages of the right-wing strategy include the following:
a) the "elite" groups may be "elite" for unfair reasons (e.g. luck; born into a rich family, despite a lack of earned merit). Or the "elitism" may be founded upon a skill which benefits merely the individual but which may have a detrimental effect on the community as a whole (e.g. an unscrupulous businessperson who may maximize profits through narcissistic and bullying disregard towards others, towards the environment, towards the law, etc.)
b) the "trickle-down" effect may not actually work in all cases. The rich may simply get richer, and the poor get poorer.
c) The strict rules may cause a rigidity to the culture which leaves various groups feeling excluded, marginalized, or persecuted.
d) The so-called "natural selection" may either occur at the cost of great suffering for many individuals, and therefore be morally intolerable--or the "natural selection" may not occur at all, paradoxically (here, the literal example would be that birth rates in highly advantaged groups are usually lower than birth rates in disadvantaged groups).
So-called "left-wing" beliefs may include the following features:
1) more flexible rules
2) an emphasis on investing society's energy in all members of the group, so as to directly support those who are struggling most. The thinking here is that if everyone is supported equally, then the entire society will flourish.
Disadvantages of the "left-wing" strategy include the following:
a) the strategy may be inefficient, and in some cases may discourage excellence. For example--by analogy but perhaps also literally--if there is a group of athletes wanting to train for the Olympics, but there are only a few trainers or facilities, the "left-wing" model might give every athlete equal training time. The star athletes would get only a mediocre ability to train, and therefore would never excel as they could have. Or, entire areas of human excellence might never be developed: space travel to the moon, heart or brain surgery, organ transplantation, etc. might never happen because they are expensive, might not be seen as efficient ways to invest energy, time, and money, and they would require the formation of a type of "elite" group (e.g. astronauts, heart surgeons, etc.). This inefficiency may certainly happen in some forms of "left-wing" economic management.
Most groups, be they nations, cities, clubs, or families, have some mixture of strategies, between the extreme "right wing" and "left wing". Perhaps part of the choice of style is determined by the cultural history of the group, though part of it could be determined by the active choice of the group.
Mind you, it seems to me that many people's positions on these matters are highly influenced by factors such as what their parents or peers think, or even by inherited predisposition--see the following twin study :
Alford, John R., Carolyn L. Funk, and John R. Hibbing "Are Political Orientations Genetically Transmitted?." American Political Science Review, 99 (2005, May): 153-167.
The study shows a significant contribution of inherited factors which influence a person's ideological stance. There are some subtleties to the findings which make the article worth a look.
An advantage to a "democratic" system is that the style could be more changeable, and that individuals don't have to be stuck permanently in a style that they don't like. A disadvantage of democratic systems is that most groups and most individuals vacillate a lot, and are often almost equally divided between "left" and "right" (e.g. look at the U.S. electorate). This can result in leadership which is itself ambivalent and unstable.
The above comments are a prelude to a metaphor I've been considering, about how the mind, or how strategizing about life, works.
A "right-wing" approach in the mind or in one's life might be to develop one's strengths, and to pay little attention to one's weaknesses, with the belief that optimizing one's strengths will optimize success in life. So if you are a talented musician but have weaker math skills and social skills, the strategy would be to practice music 12 hours per day, to skip out on math, and not to bother socializing.
A "left-wing" approach might be to divide one's day up into 30 minute blocks, and devote equal attention to music, math, socializing, knitting, soccer, cooking, etc.
Both the above approaches, in their extremes, would probably not work out very well, or whatever successes would result would come at a high cost. In the first case, we might have a brilliant but isolated, depressed, and autistic musician. In the second case, we might have a pretty well-rounded person, who however would never be able to make a career out of music, and who might carry a lifelong frustration about never having had the chance to fully develop gifts or potential.
I think most of us would agree that a moderate position between those two extremes would be most beneficial in the above example. The theoretical musician described above probably ought to practice a lot -- much more than most others -- but probably ought to spend some time struggling through some math, and trying to get involved in social activities. In the long term, such a mixed model would probably lead to even more excellence, since a well-rounded person with good morale and multiple strengths is likely to have more energy to share with society, and is less likely to be sidelined by depression. Furthermore, there can be unexpected synergistic benefits from having a broad range of experiences.
So, in my opinion, from a psychological point of view, I believe that a "moderate" position in the "political spectrum" of the mind is healthiest and most beneficial, perhaps a position which is able to flexibly assimilate ideas from both sides of an ideological spectrum.
Another phenomenon that occurs in political debate is intense polarization: opposing groups merely fight and argue with each other. The fighting and arguing rarely seem to resolve anything, but may in fact further entrench the polarization of the opposing points of view. I think it is healthy -- in the politics of the world, and the politics of the mind -- to always be on the watch for polarization, and to take active steps to diminish it. Groups of individuals tend to separate, polarize, and compete -- sports fans or athletes are one example. In can be fun to playfully feel polarized into "us" and "them" at a sports event. But it isn't fun when the polarizing occurs automatically, and interferes with problem solving, whether it be in political debate, in an argument with a loved one, or within one's own mind.
In the internal "politics" of the mind, I think it is healthy to have a clear sense of identity, to develop your positions, ideas, beliefs, values, etc. But I think it is important to watch for polarization. This may require an openness to sometimes respectfully consider ideas that seem opposed to your position.
Likewise, in world politics, I think it is important for opposing parties to work at affirming or considering the validity of their opponents' positions, to find common ground, to even find some wisdom or inspiration -- once in a while -- in the opponents' ideas.