Axiomatic module

Justified Representation

is_cohesive_for_l(profile: AbstractTrichotomousProfile, max_size_selection: int, l: int, group: AbstractTrichotomousProfile) → bool

Tests whether the given set of voters is cohesive for level l as defined in Definition 1 of Proportionality in Thumbs Up and Down Voting (Kraiczy, Papasotiropoulos, Pierczyński and Skowron, 2025).

Parameters:

• profile (AbstractTrichotomousProfile) – The trichotomous profile.

• max_size_selection (int) – The maximum number of alternatives that can be selected.

• l (int) – The required representation level.

• group (AbstractTrichotomousProfile) – The subset of voters being tested for cohesion.

Returns:

True if the group is l-cohesive, False otherwise.

Return type:

bool

all_cohesive_groups(profile: AbstractTrichotomousProfile, max_size_selection: int, min_l: int = 1, max_l: int = None, test_cohesive_func: Callable = None) → Iterator[tuple[AbstractTrichotomousProfile, int]]

Yields all voter groups that are cohesive for some level l. Yields both the group and the level l.

Parameters:

• profile (AbstractTrichotomousProfile) – The trichotomous profile.

• max_size_selection (int) – The maximum number of alternatives that can be selected.

• min_l (int, optional) – The minimum level of cohesion to test for. Defaults to 1.

• max_l (int, optional) – The maximum level of cohesion to test for. Defaults to the number of alternatives.

• test_cohesive_func (Callable, optional) – The function used to test cohesion. Defaults to is_cohesive_for_l.

Yields:

tuple of (AbstractTrichotomousProfile, int) – A cohesive group and the smallest level l for which it is cohesive.

is_base_ejr_brute_force(profile: AbstractTrichotomousProfile, max_size_selection: int, selection: Selection) → bool

Determines whether a selection satisfies Base Extended Justified Representation (Base EJR) as defined in Definition 1 of Proportionality in Thumbs Up and Down Voting (Kraiczy, Papasotiropoulos, Pierczyński and Skowron, 2025). Looks for every cohesive group and verifies that they are all satisfied.

Parameters:

• profile (AbstractTrichotomousProfile) – The trichotomous profile.

• max_size_selection (int) – The maximum number of alternatives that can be selected.

• selection (Selection) – The selection of alternatives to test.

Returns:

True if Base EJR is satisfied, False otherwise.

Return type:

bool

is_base_ejr(profile: AbstractTrichotomousProfile, max_size_selection: int, selection: Selection) → bool

Determines whether a selection satisfies Base Extended Justified Representation (Base EJR) as defined in Definition 1 of Proportionality in Thumbs Up and Down Voting (Kraiczy, Papasotiropoulos, Pierczyński and Skowron, 2025). Makes used of the close formula provided in Lemma 1 of the same paper.

Parameters:

• profile (AbstractTrichotomousProfile) – The trichotomous profile.

• max_size_selection (int) – The maximum number of alternatives that can be selected.

• selection (Selection) – The selection of alternatives to test.

Returns:

True if Base EJR is satisfied, False otherwise.

Return type:

bool

is_base_pjr(profile: AbstractTrichotomousProfile, max_size_selection: int, selection: Selection) → bool

Determines whether a selection satisfies Base Proportional Justified Representation (Base PJR) as defined in Definition 2 of Proportionality in Thumbs Up and Down Voting (Kraiczy, Papasotiropoulos, Pierczyński and Skowron, 2025).

Parameters:

• profile (AbstractTrichotomousProfile) – The trichotomous profile.

• max_size_selection (int) – The maximum number of alternatives that can be selected.

• selection (Selection) – The selection of alternatives to test.

Returns:

True if Base PJR is satisfied, False otherwise.

Return type:

bool

is_positively_cohesive_for_l(profile: AbstractTrichotomousProfile, max_size_selection: int, l: int, group: AbstractTrichotomousProfile) → bool

Tests whether a group of voters is positively cohesive for level l.

Parameters:

• profile (AbstractTrichotomousProfile) – The trichotomous profile.

• max_size_selection (int) – The maximum number of alternatives that can be selected.

• l (int) – The required representation level.

• group (AbstractTrichotomousProfile) – The subset of voters being tested.

Returns:

True if the group is positively cohesive, False otherwise.

Return type:

bool

is_positive_ejr(profile: AbstractTrichotomousProfile, max_size_selection: int, selection: Selection) → bool

Determines whether a selection satisfies Extended Justified Positive Representation (EJPR).

Parameters:

• profile (AbstractTrichotomousProfile) – The trichotomous profile.

• max_size_selection (int) – The maximum number of alternatives that can be selected.

• selection (Selection) – The selection of alternatives to test.

Returns:

True if EJPR is satisfied, False otherwise.

Return type:

bool

is_negatively_cohesive_for_l_t(profile: AbstractTrichotomousProfile, max_size_selection: int, l: int, alt_set: Iterable[Alternative], group: AbstractTrichotomousProfile) → bool

Tests whether a group of voters is l-T negatively cohesive for a given set of alternatives.

Parameters:

• profile (AbstractTrichotomousProfile) – The trichotomous profile.

• max_size_selection (int) – The maximum number of alternatives that can be selected.

• l (int) – The level of allowed violation.

• alt_set (Iterable[Alternative]) – The set of alternatives in question.

• group (AbstractTrichotomousProfile) – The subset of voters being tested.

Returns:

True if the group is l-T negatively cohesive, False otherwise.

Return type:

bool

is_group_veto(profile: AbstractTrichotomousProfile, max_size_selection: int, selection: Selection) → bool

Determines whether a selection satisfies the group veto property.

Parameters:

• profile (AbstractTrichotomousProfile) – The trichotomous profile.

• max_size_selection (int) – The maximum number of alternatives that can be selected.

• selection (Selection) – The selection of alternatives to test.

Returns:

True if the group veto condition is satisfied, False otherwise.

Return type:

bool