The Bosnian government and elections can reasonably be called "intricate".

I'll focus on the Presidency, since it seems most clear.  There are two regions: the Bosnian Federation, and Republika Serbska. These regions are defined geographically. They follow the lines of the peace agreement in 1995. Bosnians and Croats live mostly in the Federation, Serbs in the Republika. 

When a president is to be elected, the Republika choose one person, by simple plurality (person with largest number of votes wins). The Federation selects two people. Each candidate in the Federation must either enter the Croat, or the Bosnian election (It is expected that an enthnic Bosnian would not enter the Croat election, though this seems to be enforced only by tradition). Each elector must choose which election to particpate it. It is expected that electors will participate in the election that they identify most strongly with, but this isn't enforced. Two people are chosen, one to represent Croats, and one for Bosnians. 

Jewish people or other nationalities may choose to vote in either election. The former foreign minister Sven Alkalaj is Jewish, and represents a Bosnian Nationalist party. This may point to how other Jewish people chose to vote.

Then the three people elected share the presidency, with the position rotating every 8 months.

This system has been ruled to violate the European Convention on Human rights in the case *Sejdić and Finci v. Bosnia and Herzegovina*, because the presidency was guaranteed to the three major ethnicities, with Jews and Roma being excluded. At some point the country will need to change its constitution if it is to come into line with the European Convention (often seen as a prequisite for EU membership).

The upper house is elected on a ethnic basis, similar to the president, Each voter in the Federation can either vote for the Croat or for the Bosnian candidates, not for both, electing 10 members. The Republika chooses a further 5

Parliament is selected by an open list method of PR, with separate elections being held in the Federation and the Republika. This ensures that 2/3 of the members represent the Federation and 1/3 represent the republika. Multi-ethnic parties exist and field candidates in both regions, however the ethnic parties remain dominant.

sources: wikipedia and [an info booklet from the EU](http://www.europarl.europa.eu/RegData/etudes/ATAG/2015/568324/EPRS_ATA(2015)568324_EN.pdf)