In order for socialism to be possible, it must have some degree of support from the majority of the population. This does not mean that it's necessary for most people to become committed socialists. That's impossible, because most people are always apolitical, in any system. The only thing that is necessary is to have a majority of people that are willing to give socialism a shot, or who are at least not opposed to socialism. This kind of majority opinion does exist today in many capitalist countries.
Broadly speaking, there are three strategies that socialists have used or proposed for gaining power:
A. Build a socialist political party, compete in regular elections, and win.
B. Build a political party or organization focused on winning support in the streets and operating outside the framework of the existing state. When there is a wave of discontent against the existing capitalist system, organize marches and protests. If you can gather enough support for your cause to ignite widespread protests around the country, lead your comrades to break into government buildings, arrest the current leaders, and take over the state.
C. Build a trade union-like organization and, once you have enough members, organize a general strike and take over the factories and other workplaces.
Strategies A and B have been used successfully at various points in the past. Strategy C has never worked in the past, perhaps because it requires the most active involvement and carries the greatest risk for the people involved. Notice that although strategy A requires the greatest number of people to sympathise with the socialist cause, the only thing they need to do is vote - and that's a very easy, risk-free one-time deal. Strategies B and C actually require smaller numbers of sympathisers, but those sympathisers need to be a lot more actively involved - and take more risks - than in strategy A.
Of course, it's possible for the same organization to try to pursue two or three different strategies at once, and see which one seems to work best at the moment. That's the approach I support.
However, gaining power is only half of the problem. The other half is what to do once you have power. Many different socialist groups have won power in many different countries in the past, but none of them have succeeded in creating a stable socialist economic system. There have been two types of failure (again, broadly speaking):
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