Every society has a political institution because every society needs to coordinate some activities for the common good.
When we think of the "political institution" we think primarily of the state. The state has become a key institution in most 20th century societies. Individuals identify themselves in terms of state membership -- "I am an American" or "I am Japanese" -- and, in reality, the state has assumed enormous power in the lives of most individuals today.
A variety of political ideologies exist. These ideologies have different assessments of how much "coordination" of individual action is needed and for what purpose.
Some people believe that very little coordination is needed -- that individuals, if left to their own devices, will work out the compromises that are needed for a fruitful group life. No state is needed because individuals are fundamentally "equal," and will voluntarily form egalitarian communities in which group decisions are made in a democratic fashion. This political ideology is called philosophical anarchism.
Others also believe that very little coordination is needed, but they don't believe that idyllic communities will form if group control over individuals is kept to a minimum. They simply believe that individuals ought to be as free from the constraints of others as possible because such constraint serves little useful purpose. They believe that in the absence of great state power inequality is likely to flourish. But they see little wrong with this inequality because they believe that individuals are fundamentally unequal. Some individuals will abuse drugs, work little, and lead miserable lives -- and they should be free to do so. Others will pursue creative activities and live fulfilling lives -- and they should be free to do so. This libertarian position argues that so long as the actions of an individual does no direct harm to another, it should be permitted.
The 20th century is likely to be noted for the rise to prominence of two political ideology that imbued the state with great power.
Communism believes in the fundamental equality of all individuals, and believes that significant state power is often needed to insure that individuals share equally the bounties produced by society. The pursuit of a classless society and its preservation are the preeminent purpose of the powerful state under communism.
Fascism also believes
in
great state power, but not for the reason of bring about egalitarian
conditions
or a classless society. Fascists believe that the
group
-- the "Fatherland," the "race" -- is of intrinsically greater worth
than
the individual. The interest of the "Fatherland" is of preeminent
importance and each individual, to the best of his or her ability,
ought
to work toward that end. Inequality is presumed to exist
among
individuals, but all individuals should employ their varied abilities
to
further the group's interest.
Look at the table below and think about your
personal
political ideology. Can you place "your point" on this
table?
How equal do you think individuals are? Are you high up the "Y"
axis
or low down? How much power do you think the state should
have?
Are you over toward the "high" end on the "X" axis or are you over
toward
the "low" end?

This chart comes from Daniel Chirot's Social
Change in the Modern Era (1986: 145).
American political parties -- the Democrats and Republicans -- both would have to be place toward the center of this table. You can decide where their exact placement ought to be?