1892: No candidate wins a majority

[bee33]

What if the 1892 election was deadlocked between Cleveland, Harrison, and Weaver?

[Skill and Chance]

IRL Democrats had a huge House majority and controlled 25/44 state delegations, so they would be able to elect Cleveland unilaterally.  If you assume some uniform swing away from Democrats, its possible they could lose their 1-seat majorities in OH and WI along with the very close race for WY-AL, in which case they are down to 22/44 and a deal has to be made. The Populists controlled the state delegations in CO and KS, and they held the decisive 7th seat in the California delegation which was split 3R/3D/1P.

By far the most likely outcome is that the deal between the Populists and Democrats happens 3 years earlier than IRL and they elect Cleveland in the House in exchange for several policy concessions. 

The Senate was 42D/38R/3P IRL, so it's very possible that Democrats would need the Populists to pick the VP in the Senate as well, assuming Republicans and Populists do a bit better in the state legislatures.