Majority rule automaton
Voters that take the majority opinion of their neighbourhood, which coarsens into domains.
- Name:
majority_rule - Field:
social/opinion_dynamics - Formalism: lattice dynamics
- References: Argun et al. 2021; Gärtner and Zehmakan 2017
Select this system
from skcomplex.systems import create_simulation, create_system, describe
system = create_system('majority_rule')
entry = describe('majority_rule')
trajectory = create_simulation('majority_rule').prepare().run().trajectory_
Factory
@register_system(
field='social/opinion_dynamics',
tags=('lattice', 'opinion', 'voting'),
references=('Argun et al. 2021', 'Gärtner and Zehmakan 2017'),
defaults={'until': 50, 'dt': 1},
)
def majority_rule(
shape: Sequence[int] = (100, 100),
*,
density: float = 0.5,
random_state: int | np.random.Generator | None = 0,
) -> System:
"""Return voters that take the majority opinion of their neighbourhood, which coarsens into domains.
Every step every voter takes the opinion of the majority of its eight Moore neighbours and keeps its own when they
tie, the majority rule of Argun et al. (2021, section 4.3).
Args:
shape:
The number of rows and columns.
density:
The probability that a voter starts with opinion 1.
random_state:
The seed or generator of the initial opinions.
Returns:
system:
The system, with the opinions `voters.opinion`.
Examples:
>>> from skcomplex.systems.social.opinion_dynamics import majority_rule
>>> majority_rule((10, 10)).elements[0].prepare().size_
100
"""
values = _random_cells(shape, density, random_state)
return System(
elements=[
LatticeElement(
'voters',
element=MajorityVoterElement,
space=LatticeSpace(tuple(shape)),
values={'opinion': values},
),
],
interactions=[
LocalRuleInteraction(
'majority',
target='voters',
state='opinion',
rule=TotalisticSpec(_is_majority),
neighborhood=MooreNeighborhood(center=True),
),
],
)
Components
Elements:
MajorityVoterElement, fromElement
Interactions:
LocalRuleInteraction
class MajorityVoterElement(Element):
"""Cell that takes the majority opinion of its Moore neighbourhood, itself included.
The majority rule is a `LocalRuleInteraction` of the lattice, which `majority_rule` adds.
Args:
label:
The label of the cell or the lattice group.
visual:
How the agent is drawn, or `None` for `default_visual_`.
opinion:
The initial opinion, 0 or 1.
Examples:
>>> from skcomplex.systems.social.opinion_dynamics import MajorityVoterElement
>>> MajorityVoterElement('cell', opinion=1).opinion
1
"""
def __init__(
self,
label: str,
visual: VisualSpec | None = None,
*,
opinion: Annotated[float, StateSpec(domain=FiniteEnumeratedSet([0, 1]))] = 0,
) -> None:
super().__init__(label, visual=visual)
self.opinion = opinion
class LocalRuleInteraction(Interaction):
"""Local rule of a cellular automaton, which sets the next value of every cell from its ordered neighbourhood.
The rule is a table of the next value of every configuration of the neighbourhood, `TableSpec`, a rule of the sum
of the neighbourhood, `TotalisticSpec`, a rule of the cell and the sum of its neighbours, `OuterTotalisticSpec`, an
object whose `table()` returns a `TableSpec`, or a function. A function receives one array per neighbour of every
read state, in neighbourhood order, with one value per cell, the uniform array `random` when the rule is stochastic,
and the parameters of the bound group it names, and returns the next values of the states, one array per state. A
state of several components per cell, such as a truncated power series of `PowerSeriesSpec`, reaches a function as
one row of components per cell. A `StateTranslationNeighborhood` reads a group space at the product of every site
and the group element that the first read state holds there.
Args:
label:
The label of the interaction, unique among the parts of its system.
target:
The path of the group on the cells of a lattice, the nodes of a network, or a Cayley graph.
state:
The name of the state the rule sets, or a tuple of the names of the states it sets together.
rule:
The table, the totalistic rule, or the function.
neighborhood:
The ordered neighbourhood of every cell, such as `VonNeumannNeighborhood(center=True)`.
reads:
The names of the states whose neighbourhoods a function reads, or `None` for the states it sets.
schedule:
`'synchronous'`, `'random-sequential'`, `'random-site'`, `'checkerboard'`, or `'colored'`.
stochastic:
Whether a function receives the uniform random array `random`.
Raises:
ValidationError:
The state or the read states are not names, or the neighbourhood is not a neighbourhood.
Examples:
>>> from skcomplex.core.components.interactions import LocalRuleInteraction
>>> from skcomplex.core.components.spaces import VonNeumannNeighborhood
>>> from skcomplex.core.specs import TotalisticSpec
>>> parity = TotalisticSpec({1: 1, 3: 1})
>>> around = VonNeumannNeighborhood(n_dim=1, center=True)
>>> rule = LocalRuleInteraction('parity', target='cells', state='cell', rule=parity, neighborhood=around)
>>> rule.schedule
'synchronous'
"""
law_classes: ClassVar[tuple[type[BaseLaw], ...]] = (LocalRuleLaw,)
def __init__(
self,
label: str,
*,
target: Annotated[str, RoleSpec(elements=(ElementKind.ANY,), states=('state', 'reads'))],
state: str | tuple[str, ...],
rule: object,
neighborhood: BaseNeighborhood,
reads: Sequence[str] | None = None,
schedule: str = 'synchronous',
stochastic: bool = False,
) -> None:
super().__init__(label)
self.target = target
self.state = state
self.rule = rule
self.neighborhood = neighborhood
self.reads = reads
self.schedule = schedule
self.stochastic = stochastic
def _get_names(self) -> tuple[str, ...]:
"""Return the names of the states the rule sets."""
return (self.state,) if isinstance(self.state, str) else tuple(self.state)
def _check(self) -> None:
"""Raise an error for states that are not names, or a neighbourhood that is not one.
Raises:
ValidationError:
The state or the read states are not names, or the neighbourhood is not a neighbourhood.
"""
super()._check()
names = [*self._get_names(), *(self.reads or ())]
if not names or not all(isinstance(name, str) and name.isidentifier() for name in names):
error_msg = f'The local rule {self.label!r} sets {self.state!r} and reads {self.reads!r}. Give state names.'
raise ValidationError(error_msg)
if not isinstance(self.neighborhood, BaseNeighborhood):
error_msg = f'The neighbourhood of the local rule {self.label!r} is {self.neighborhood!r}. Give one.'
raise ValidationError(error_msg)
def _get_laws(self, namespace: SimpleNamespace) -> list[BaseLaw]:
"""Return the local rule law of the states of the target.
Args:
namespace:
The namespace of the symbols the laws can use, with `namespace.target`.
Returns:
laws:
The local rule law.
"""
targets = tuple(getattr(self._get_member(namespace, 'target'), name) for name in self._get_names())
reads = (
None
if self.reads is None
else tuple(getattr(self._get_member(namespace, 'target'), name) for name in self.reads)
)
return [
LocalRuleLaw(
targets[0] if isinstance(self.state, str) else targets,
self.neighborhood,
self.rule,
reads=reads,
schedule=self.schedule,
stochastic=self.stochastic,
label=self.label,
),
]