.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/consensus/pos/plot_01_stake.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_api_gallery_consensus_pos_plot_01_stake.py>`
        to download the full example code or to run this example in your browser via JupyterLite.

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_api_gallery_consensus_pos_plot_01_stake.py:


Proof of stake: a stake-weighted proposer lottery (Peercoin 2012)
=================================================================

Weighting proposer selection by stake changes the resource used to allocate
influence. This sampler isolates that one mechanism; it has no voting,
slashing, randomness beacon, or finality and is not a full PoS protocol.

What to look for
----------------

Compare observed selection frequencies with stake proportions. More trials tend to bring
them closer; splitting one stake among names does not increase its combined expected
share.

Read cells in order. An ``assert`` that produces no output has passed.
The final exercise asks you to change an input and explain the result.

The history behind this experiment: :doc:`/history/consensus_breakthroughs`.
See :doc:`/exercises/consensus` for a worked solution to the exercise.

.. GENERATED FROM PYTHON SOURCE LINES 24-39

.. code-block:: Python

    from collections import Counter

    import matplotlib.pyplot as plt

    import blockchainkit as bk

    stakes = {"alice": 10, "bob": 30, "carol": 60}
    rounds = 10_000
    proposers = bk.consensus.StakeSampler(stakes, seed=42).sample(rounds)
    assert proposers == bk.consensus.StakeSampler(stakes, seed=42).sample(rounds)
    counts = Counter(proposers)
    expected = [stake / sum(stakes.values()) for stake in stakes.values()]
    observed = [counts[name] / rounds for name in stakes]
    print("Observed selection fractions:", dict(zip(stakes, observed, strict=True)))





.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    Observed selection fractions: {'alice': 0.0938, 'bob': 0.2949, 'carol': 0.6113}




.. GENERATED FROM PYTHON SOURCE LINES 40-42

Stake concentration is visible even when the lottery is fair
------------------------------------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 42-55

.. code-block:: Python

    fig, ax = plt.subplots(figsize=(7, 4))
    xs = list(range(len(stakes)))
    ax.bar([x - 0.18 for x in xs], expected, 0.36, label="Stake fraction")
    ax.bar([x + 0.18 for x in xs], observed, 0.36, label="Observed proposer fraction")
    ax.set(
        xticks=xs,
        xticklabels=list(stakes),
        ylabel="Fraction",
        title="Seeded proposer sampling over 10,000 rounds",
    )
    ax.legend()
    fig.tight_layout()




.. image-sg:: /api/gallery/consensus/pos/images/sphx_glr_plot_01_stake_001.png
   :alt: Seeded proposer sampling over 10,000 rounds
   :srcset: /api/gallery/consensus/pos/images/sphx_glr_plot_01_stake_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 56-62

Exercise
--------
Split Carol's stake across ten names. Does her total expected influence
change? Why is choosing a proposer insufficient to decide between two
conflicting blocks that proposer might sign? Why is a public seed unsuitable
as the sole randomness mechanism for a live consensus protocol?


.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (0 minutes 0.154 seconds)


.. _sphx_glr_download_api_gallery_consensus_pos_plot_01_stake.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: lite-badge

      .. image:: images/jupyterlite_badge_logo.svg
        :target: ../../../../lite/lab/index.html?path=api/gallery/consensus/pos/plot_01_stake.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: plot_01_stake.ipynb <plot_01_stake.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: plot_01_stake.py <plot_01_stake.py>`

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: plot_01_stake.zip <plot_01_stake.zip>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_