(Weighted) Majority Graphs
=======================================

A **majority graph** is a directed asymmetric graph in which the nodes are the candidates and an edge from $a$ to $b$ means that $a$ is majority preferred to $b$. 

```{eval-rst}

A :class:`~pref_voting.weighted_majority_graphs.MajorityGraph` has a number of methods used by voting methods. 

.. exec_code::

    from pref_voting.weighted_majority_graphs import MajorityGraph

    mg = MajorityGraph([0, 1, 2], [(0, 1), (1, 2), (2, 0)])

    print(mg.edges)
    for c1 in mg.candidates:
        for c2 in mg.candidates: 
            print(f"{c1} is majority preferred to {c2}: {mg.majority_prefers(c1, c2)}")
            print(f"{c1} is tied with {c2}: {mg.is_tied(c1, c2)}")

    for c in mg.candidates:
        print(f"The dominators of {c} are {mg.dominators(c)}")
        print(f"The candidates that {c} dominates are {mg.dominates(c)}")
    
    print(f"Copeland scores: {mg.copeland_scores()}")
    print(f"Condorcet winner: {mg.condorcet_winner()}")
    print(f"Weak Condorcet winners: {mg.weak_condorcet_winner()}")
    print(f"Condorcet loser: {mg.condorcet_loser()}")

    print()

    mg2 = MajorityGraph([0, 1, 2], [(0, 1), (1, 2)])

    print(mg2.edges)
    for c1 in mg2.candidates:
        for c2 in mg2.candidates: 
            print(f"{c1} is majority preferred to {c2}: {mg2.majority_prefers(c1, c2)}")
            print(f"{c1} is tied with {c2}: {mg2.is_tied(c1, c2)}")

    for c in mg2.candidates:
        print(f"The dominators of {c} are {mg2.dominators(c)}")
        print(f"The candidates that {c} dominates are {mg2.dominates(c)}")
    
    print(f"Copeland scores: {mg2.copeland_scores()}")
    print(f"Condorcet winner: {mg2.condorcet_winner()}")
    print(f"Weak Condorcet winners: {mg2.weak_condorcet_winner()}")
    print(f"Condorcet loser: {mg2.condorcet_loser()}")

```

A **margin graph** is a weighted directed asymmetric graph in which the nodes are the candidates, an edge from $a$ to $b$ means that $a$ is majority preferred to $b$, and the weight of the edge is the margin of $a$ over $b$. 

```{eval-rst}

A :class:`~pref_voting.weighted_majority_graphs.MarginGraph` has a number of methods used by voting methods. 

.. important:: 

    The weights of a MarginGraph can be any numbers.  However, if the weights are generated by a profile of linear orders, then the weights will have the same parity (which is even if there is any zero margin between distinct candidates). 

.. exec_code::

    from pref_voting.weighted_majority_graphs import MarginGraph

    mg = MarginGraph([0, 1, 2], [(0, 1, 1), (1, 2, 3), (2, 0, 3)])

    print(mg.edges)
    for c1 in mg.candidates:
        for c2 in mg.candidates: 
            print(f"the margin of {c1} over {c2} is {mg.margin(c1, c2)}")
            print(f"{c1} is majority preferred to {c2}: {mg.majority_prefers(c1, c2)}")
            print(f"{c1} is tied with {c2}: {mg.is_tied(c1, c2)}")

    for c in mg.candidates:
        print(f"The dominators of {c} are {mg.dominators(c)}")
        print(f"The candidates that {c} dominates are {mg.dominates(c)}")
    
    print(f"Copeland scores: {mg.copeland_scores()}")
    print(f"Condorcet winner: {mg.condorcet_winner()}")
    print(f"Weak Condorcet winners: {mg.weak_condorcet_winner()}")
    print(f"Condorcet loser: {mg.condorcet_loser()}")

```



```{eval-rst}

Both :class:~pref_voting.weighted_majority_graphs.MarginGraph` and :class:~pref_voting.weighted_majority_graphs.MajorityGraph` can be generated from a profile.

.. exec_code::

    from pref_voting.profiles import Profile 
    from pref_voting.profiles_with_ties import ProfileWithTies 

    prof = Profile([[0, 1, 2], [2, 0, 1], [1, 0, 2]], rcounts=[2, 1, 2])

    prof.display()

    majg = prof.majority_graph()
    print(f"The majority graph edges are {majg.edges}")

    mg = prof.margin_graph()
    print(f"The margin graph edges are {mg.edges}")

    prof2 = ProfileWithTies([{0: 1, 1: 2, 2: 3}, {1:1, 2:1, 0:2}, {2:1, 0:2}], [2, 3, 1])
    prof2.display()

    majg = prof2.majority_graph()
    print(f"The majority graph edges are {majg.edges}")

    mg = prof2.margin_graph()
    print(f"The margin graph edges are {mg.edges}")
    
```


## MajorityGraph Class

```{eval-rst}
.. autoclass:: pref_voting.weighted_majority_graphs.MajorityGraph
    :members: 
```

## MarginGraph Class

```{eval-rst}
.. autoclass:: pref_voting.weighted_majority_graphs.MarginGraph
    :members: 
    :show-inheritance:
```

## SupportGraph Class

```{eval-rst}
.. autoclass:: pref_voting.weighted_majority_graphs.SupportGraph
    :members: 
    :show-inheritance:
```