Socialism, as defined by me (though I think my understanding is fairly sound) is basically the political and economic philosophy that maintains that all members of a society are working toward a common good that is to be selected democratically. Following from this premise is that since everyone is working toward the same goal, then everyone is to be equal by sharing in the same goal, the common goal. Also following is that since the political and economic goals have been selected democratically, then the people and the community, the people and the government, are the same. Therefore, the common goals toward which all society is working, as selected by the people, are equally selected by the state. The emphasis is on the group, rather than the individual. The details that manifest, things like affirmative action, wage and price fixing (unions), government control of means of production, etc., all these things follow from the basic premise of a common goal.
I agreed already that Jews moved leftward as a reaction to right wing antisemitism, which permeated both the private and the public sides of European and American life. In my view, it is the emphasis on equality that was the attraction, since societies traditionally have relegated Jews to a less than equal place, although I'm sure the other aspects of socialism were also attractive to those who could be idealists, as they continue to be the world over to many peoples. I personally think that moving to traditional liberalism would have made more sense, though. In fact, I believe that the remnants of tradtional liberalism that still cling to modern liberalism are an attractant for Jews.
Yes, I think it's a great paradox that a left leaning segment of the population is also one of the most capitalist segments. Of course, I understand that Jews became capitalists because landowning, and many of the professions, were traditionally prohibited to them.
In conclusion there is no "...Jewish tradition of cherishing leftism".