The Bosnian government and election processeselections can reasonably be called "intricate".
I'll focus on the Presidencypresidency, since it seems most clear. There are two regions: the Bosnian Federation of Bosnia and Herzegovina ("Federation"), and Republika SerbskaSrpska ("RS"). These regions are defined geographically. They follow the lines of the peace agreement in 1995. BosniansBosniaks and Croats live mostly in the Federation, Serbs in the RepublikaRS.
When a Presidentpresident is to be elected, the Republika chooseRS chooses one person, by simple plurality (personthe person with largest number of votes wins). The Federation selects two people. Each candidate in the Federation must either enter either the Croat, or the BosnianBosniak election (Itit is expected that an ethnic BosnianBosniak would not enter the Croat election, and vice versa, though this seems to be enforced only by tradition). Each elector must choose which election to participate itin. It is expected that electors will participate in the election that they identify most strongly with, but this also isn't enforced. Two people are chosen,: one to represent Croats, and one for BosniansBosniaks.
Jewish people or other nationalities may choose to vote in either election. The former foreign minister Sven Alkalaj is Jewish, and represents a Bosnian NationalistBosniak nationalist party. This may point to how other Jewish people chose to vote.
Then theThe 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 (ECHR) in the case Sejdić and Finci v. Bosnia and Herzegovina, because the Presidencypresidency was guaranteed to the three major ethnicities, with Jews and Roma being excluded. At some point the country will need to change its Constitutionconstitution if it is to come into line with the European ConventionECHR (often seen as a prerequisite for EU membership).
The Upper Houseupper house of the legislature is elected on aan ethnic basis, similar to the President;presidency; each voter in the Federation can either vote for the Croat or for the BosnianBosniak candidates, not for both, electingboth; the Federation elects 10 members. The RepublikaRS chooses an additional 5 representativesmembers.
ParliamentThe lower house is selected by an open list method of PR, with separate elections being held in the Federation and the RepublikaRS. This ensures that 2/3 of the members represent the Federation and 1/3 represent the RepublikaRS. 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.