Party of Democratic Action
Yet some experts, officials and diplomats say future elections are almost irrelevant while local leaders continue to block the system, playing their lose-lose games.
To make matters worse, Bosnia's unfolding political drama is increasingly intertwined with other regional and international disputes, especially with the tensions between Serbia and Kosovo.
They warn that years of political divisions, zero-sum games, distrust and poor communication between local leaders, as well as growing tensions among key regional and global actors, have left Bosnia a ticking time-bomb that could go off at any moment, leading to the collapse of the remaining joint institutions or even the breakup of the country.
Bosniak Sefik Dzaferovic (R) and Croat Zeljko Komsic (2-R), members of the presidency. EPA-EFE/FEHIM DEMIR
The presidency - comprising a Bosniak, Serb and Croat - was unable to agree the agenda for Tuesday's session and so postponed the meeting and a decision on appointing a prime minister, or the chair of the Council of Ministers.
Turkish President Recep Tayyip Erdogan is visiting the Bosnian capital of Sarajevo on July Tuesday and Wednesday to attend the regional Summit of the South-East European Co-operation Process, SEECP.
However, according to agreed protocols, he will also use this visit to meet Bosnian and regional leaders.
Bosnia and Herzegovina will be suspended from the work of the Parliamentary Assembly of the Council of Europe, the PACE, for failing to appoint new representatives to that body.
According to the Council of Europe's Rules, member states must nominate new delegations to the Parliamentary Assembly within six months of the day of an election.