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This chapter is largely taken up with the conversation between Sviyazhsky, Levin, the older landowner, and Mikhail Petrovich, the second landowner.
The older landowner comments that he lives at home, doesn't buy anything, and doesn't rent anything. He thinks that the peasants are running wild into drunkenness because everything is individually owned. The old feudal system, in which village ploughing and farming was for the good of the group (under the authority of the nobility) is gone. When his peasants run wild and he turns them in to the new-fangled justice of the peace, they just get acquitted. It's all seems useless. (He's teasing Sviyazhsky, and Sviyazhsky takes the joke.)
Mikhail Petrovich says, that some of the peasants are shameless, but for the most part, he's got a rational system going: he loans them enough money to pay the first third of their taxes, and gets them to work for him in exchange, sowing oats, making hay, and so on.
Levin's disappointed with this patriarchal method, and asks the old landowner how he gets his work done.
The landowner replies that everything has gone to the dogs since the emancipation of the serfs (in 1861, under Czar Alexander II). Before then, landowners were able to carry on their own improvements to farming tools and methods. Now, without that authority over the peasants, everything is sinking into a primitive condition. Without a feudal relationship, you can't make the hired help do anything right.
Levin's not so interested in the landowner's proposal for how to liberate himself from this decline in farming (and the novel doesn't go into detail on that point) but he definitely agrees that the quality of farming is dying down.
Sviyazhsky finally gets serious, saying that the quality of farming when the serfs were around was actually low because they didn't have machinery or good accounting systems. Now that there are banks and, more money can be invested into farming.
Levin disagrees adamantly. He's spent tons of money improving farming and has gotten nowhere. The new livestock were lost, his new tools have been lost. What's more, says Levin, all wealthy farmers who conduct their business on rational principles operates on a loss.
Sviyazhsky replies that his (Levin's) farm might not be profitable, but that isn't necessarily due to agricultural methods. It could just be because Levin is a bad manager.
Sviyazhsky blocks Levin from probing his mind too deeply, and heads out of the room before he gets caught up too much in the discussion.
Levin and the old landowner get into a discussion about the appropriate relationship with peasants. Levin wants to know why true partnership between the nobility and peasantry is impossible. The landowner replies that such a thing would be impossible with the Russian muzhik, who needs the stick of authority to make him do anything.
Sviyazhsky returns, having smoked a cigarette, and says, serfdom is a barbaric institution. What we need now are new forms of community that have been defined and accepted in Europe.
Levin wonders why there can't be a uniquely Russian form. What if these newly invented European ways don't suit the Russian context? This brings the argument to a standstill, because Sviyazhsky can't answer, and starts fumbling with terms he doesn't explain. The two landowners take their leave, and Sviyazhsky uses this as a pretext to end his discussion with Levin.