(Note for LessWrong: This is more overtly about partisan politics than the norm, but I think it's not more about that than The Two-Party Swindle, from the Sequences, and it proposes a structural model that doesn't require people to be as stupid.)
There are a few points I didn't make in my post on blame games because they seemed extraneous to the core point, which are still important enough to write down.
The Hierarchy game is a zero-sum game in which people closer to the center expropriate from people farther from the center, and use some of those resources to perpetuate the power imbalances that enable the expropriation. Players that fail to submit to expropriation by higher-level players are punished by those more-powerful players, often through intermediaries. Players that fail to help members of their class expropriate from those beneath them are excluded from their class, and often coordinated against more overtly.
This game isn't inherently majoritarian, - instead, it allows smaller groups to stably expropriate from larger ones, because every player has a short-run incentive to go along with the arrangement. Feudalism is a simple example of the hierarchy game. Modern states almost always have some hierarchical arrangements, such as the police and military, and (less formally) economic class.
Around the time of the French revolution - a replacement of Feudal arrangements with Modern states - people started using terms like "left" and "right" to refer to political orientations. These terms are related to natural structural coalitions within a modern democratic state.
Political parties don't overtly promise to expropriate from 49% on behalf of an arbitrary 51%. This is probably in part because this would be correctly viewed as a proposal to massively increase expropriative activity relative to other activity, accelerating the rate of expropriation, which actually isn't in the majority's interests, and would quickly undermine the democratic paradigm without providing a replacement to enforce property claims. Instead, appropriation is opportunistic, and political coalitions seem to be oriented around natural power bases which could in principle replace deliberative democracy.
One natural sort of organization to orient around is the formal hierarchy with a monopoly on force - the military and police. The staffing needs of these organizations are substantial, especially in wartime (democracies perform well in wars in part because of their ability to mobilize a large share of the population without destabilizing their internal political arrangement) so they already form a natural constituency.
The obvious advantage of control over these organizations is in the event of a civil war, control over the army and police would be a massive advantage. So, building a group identity around those things is a pretty plausible way to expropriate the country from the other half.
The "right wing" is the part of the political spectrum that most resembles or is most naturally allied with this coordination strategy. Generally, if there's an identifiable majority group (ethnic, cultural, religious, etc.), the hierarchy of violence will perceive members of that group as more "central" and want to help them expropriate from minority groups more than vice versa, insofar as gaps in the rule of law allow this. People rewarded by the existing credit-allocation, the "upper classes," will also tend to favor and be favored by this arrangement.
The "left wing" is the natural complement to this strategy: a political "big tent" made up of all the noncentral groups. Such a coalition has a structural advantage as long as democratic institutions persist, since any new group (e.g. immigrants) that isn't part of the majority is a natural member of the "left wing" coalition. Such groups also tend to seek control of, and expropriate resources through, the parts of the state that are responsible for information processing, investment, and resource allocation rather than the administration of violence. In short, the bureaucracies and those who staff them.