def METHOD_NAME(self, debate_constraints):
    """Allocates venues for debates that have one or more constraints on
    them. `debate_constraints` should be
    For each debate, it finds the set of venues that meet all its
    constraints, or if that set is empty, then it satisfies as many
    constraints as it can, with higher-priority constraints taking absolute
    precedence over lower-priority constraints. It then chooses a random
    venue from the preferred venues in that set, or if there are no
    preferred venues, then from all venues in that set.
    It runs through debates in descending order of priority, where the
    priority of a debate is the priority of its highest-priority constraint.
    """
    debate_venues = dict()
    while len(debate_constraints) > 0:
        debate, constraints = debate_constraints.pop(0)
        highest_constraint = constraints.pop(0)
        eligible_venues = set(highest_constraint.category.venues.all()) & set(self._all_venues)
        # If we can't fulfil the highest constraint, bump it down the list.
        if len(eligible_venues) == 0:
            logger.debug("Unfulfilled (highest): %s", highest_constraint)
            if len(constraints) == 0:
                logger.debug("%s is now unconstrained", debate)
                continue  # Failed all constraints, debate is now unconstrained
            new_priority = constraints[0].priority
            for i, dc in enumerate(debate_constraints):
                if new_priority >= dc[1][0].priority:
                    break
            else:
                i = 0
            debate_constraints.insert(i, (debate, constraints))
            continue
        # If we get this far, we have at least one eligible venue.
        # Find the set of eligible venues satisfying the best set of constraints.
        satisified_constraints = []
        for constraint in constraints:
            if any(sc.subject == constraint.subject for sc in satisified_constraints):
                continue  # Skip if we've already done a constraint for this subject
            constraint_venues = set(constraint.category.venues.all())
            if eligible_venues.isdisjoint(constraint_venues):
                logger.debug("Unfilfilled: %s", constraint)
            else:
                eligible_venues &= constraint_venues
                satisified_constraints.append(constraint)
        # If no eligible venues are preferred venues, drop the last preferred venue.
        preferred_venues = set(self._preferred_venues)
        if eligible_venues.isdisjoint(preferred_venues):
            logger.debug("No preferred venues available: %s", debate)
            self._preferred_venues = self._preferred_venues[:-1]
        else:
            eligible_venues &= preferred_venues
        # Finally, assign the venue.
        venue = random.choice(list(eligible_venues))
        debate_venues[debate] = venue
        self._all_venues.remove(venue)
        if venue in self._preferred_venues:
            self._preferred_venues.remove(venue)
        logger.debug("Assigning %s to %s", venue, debate)
    return debate_venues