Mapping Brexit II

An updated map of Monday’s Indicative Votes but including last week’s votes for the Withdrawal Agreement. Note more analysis here:
http://www.duncanrobertson.com/2019/03/28/mapping-brexit/

This network map shows each MP that voted for each of 5 propositions: Parliamentary Sovereignty, Confirmatory Public Vote, Customs Union, Common Market 2.0, or the Withdrawal Agreement. The large dots show the number of MPs that voted for each proposition. It shows that Parliamentary Sovereignty and the Confirmatory Public Vote are unlikely to be in any consensus (unless with Common Market 2.0 &/or Customs Union), whereas a consensus between the Withdrawal Agreement and either Common Market 2.0 &/or Customs Union may be a possible way to form a Parliamentary majority.

Note the colours are indicative only, and that these votes were whipped by either the Labour Party or the Conservative Party (for instance, Cabinet ministers were instructed to vote only for the Withdrawal Agreement, so the blue dots to the right of the Withdrawal Agreement dot are likely to include the Cabinet).

Mapping Brexit

Wednesday’s indicative votes in the House of Commons produced no definitive answer of the way forward.  By using social network analysis showing the size of each voting bloc and ‘Hamming distances’ (ironically usually used for error correction), we can map how close MPs are to each other, giving an indication of how a coalition could be made if each block of MPs flipped their vote in order to form a Parliamentary consensus.

Brexit is currently turning out to a failed experiment in direct democracy, something I pointed out nearly three years ago.

However, with the House of Commons opening up data, it does allow us a rare insight into the goings on of the population and the MPs that are our representatives.

One interesting data source is released by the UK Parliament showing the voting record of every MP for every ‘division’ (vote). One particularly interesting vote was that done on Wednesday 27 March, where MPs were able to cast their votes for 8 motions:

Mr Baron’s motion B (No deal) ,
Nick Boles’s motion D (Common market 2.0) ,
George Eustice’s motion H (EFTA and EEA) ,
Mr Clarke’s motion J (Customs union) ,
Jeremy Corbyn’s motion K (Labour’s alternative plan) ,
Joanna Cherry’s motion L (Revocation to avoid no deal) ,
Margaret Beckett’s motion M (Confirmatory public vote) , and
Mr Fysh’s motion O (Contingent preferential arrangements)

By making a so-called bipartite network, we can map individual MPs to the votes for which they voted yes. This results in a map of MPs shown below.

(c) Dr Duncan Robertson duncanrobertson.com

While this is interesting, it doesn’t really show the distance between MPs’ voting intentions.

We can redraw the map by using the distance between MPs according to the votes they cast. We can do this by constructing a binary string of their votes. For simplicity, we count only the ‘aye’ or yes votes, and ignore abstentions and nos.

For instance, if an MP voted yes, no, no, yes, no, yes, yes, no, they would be given a string of 10010110, whereas if another MP voted no, no, yes, no, yes, yes, no, yes, they would be given a string of 00101101. So, what is the ‘distance’ between 10010110 and 00101101? For this, we use the Hamming distance – count the number of locations where there is a difference. In this case, the Hamming distance between the MPs is 6.

By constructing a graph of Hamming distances of 1, we can construct neighbours of individual groups of MPs. This is shown in the graph below.

I have listed the votes in the following order:

Common Market 2.0
Confirmatory Public Vote
Contingent Preferential Arrangement
Customs union
EFTA and EEA
Labour’s Alternative Plan
No Deal
Revocation to Avoid No Deal

(c) Dr Duncan Robertson duncanrobertson.com

However, this isn’t very useful, as it doesn’t show the type of MP that voted for each of these. So we can relabel the nodes with a representative MP from that bloc.

From this, you can work out the number of intermediate MPs to get to any other MPs. What is quite interesting is that every MP was just one vote away from another – no-one is isolated. Which, in some little way, gives us hope.

(c) Duncan Robertson duncanrobertson.com

We can then weight the edges to show the possible coalition that could be made if these blocs were to join. And here it is:

The size of each circle represents the number of MPs that voted the same way as the representative MP named on the circle, and the thickness of the links shows how many MPs would join together if one vote were flipped.

If the linked blocs join up, you can see how there could be a path to a Parliamentary majority – for the blocs to join, it would mean switching one vote from ‘aye’ to ‘no’ or vice versa.

For completeness, the list of MPs and their associated binary string is linked here. You can find the MPs that are part of each bloc by searching for the MP name in the label on the network graph. The Hamming distance between each and every MP is available on request. I leave it to the reader to construct an affinity matrix – or what I would call currently describe as a ‘Matrix of Hate’ for each MP pair.

The Conservative Manifesto: Care Fees as a Percentage of Initial Wealth

The Conservative Party have announced their manifesto for the 2017 General Election.  Included in this (on page 64-65) is proposed

We will introduce a single capital floor, set at £100,000, more than four times the current means test threshold. This will ensure that, no matter how large the cost of care turns out to be, people will always retain at least £100,000 of their savings and assets, including value in the family home.

A quick calculation on the effective ‘Tax’ (Care Fees as a Percentage of Initial Wealth) shows the following distribution of Tax Rates.  On the x axis is initial wealth (the value of your house plus any savings), and on the y axis is the Tax Rate.  The Conservative Party have since augmented this plan with a proposed cap (consultation to come).

Values used for Care Fees: £20,000, £40,000, £60,000, £80,000; £100,000.  Values used for Initial Wealth: £0, £100,000, …, £1,000,000.  The trend continues downwards after this figure.

As many have pointed out, this affects individuals with initial wealth just over £100,000 proportionately far more than those with higher initial wealth.  More detail on policy options for funding social care can be found in the Dilnot Commission report and a summary of their proposals is shown below:

 

Eight Mile and the Emergence of Segregation

Eight Mile, epitomized by Eminem in the film of the same name, is a street in Detroit that marks the boundary between the majority white northern suburbs and the majority black neighborhoods closer to the inner city.

But what causes this segregation in the first place?

Hypothesis 1: The Central Planner

Zoning Map, 1930s, showing HOLC zoning, source: http://www.urbanoasis.org/projects/holc-fha/digital-holc-maps/

In Detroit’s case, as with many cities across the USA, it was, in part, due to the zoning of the city by the federal Home Owners’ Loan Corporation, which zoned the city into areas of risk, meaning that banks were indirectly encouraged to develop outer suburbs while not offering mortgages to inner city properties.  This lead to wealthier, generally white, residents moving to the suburbs.

Indeed, physical barriers, such at the Detroit Wall, also known as the Eight Mile Wall, were built to separate majority black and majority white neighborhoods.

Detroit Today

The legacy of these zones live on today, as seen in the map below from the 2010 US Census.  The dividing line between the green (black) areas and the blue (white) areas is Eight Mile Road.

DotMap http://demographics.virginia.edu/DotMap/ based on 2010 US Census

 

 

So, segregation exists, and is caused by a central actor. But is there an alternative explanation?

Alternative Hypothesis: Emergence

In 1971, Thomas Schelling set out to model the phenomenon, not by assuming a central planner, but by modelling the interactions of individuals.

Thomas Schelling’s model was this.  Assume individuals are placed in a grid, similar to being located on a chess board.  Allow individuals who are in a local minority to move.  In the example below, the blue circle is in a minority (with 5 out of its 6 neighbors being a different color), and according to the rules of the model, is unhappy.  It could decide to move to the vacant square to the north-west, but it would still be in a local minority (with 4 out of 6 neighbors being a different color) and would remain unhappy.  So instead, it chooses the space to the south west where 3 out of its 6 neighbors are of the same color, and not being in a minority, it settles there.

Agent Movement © Duncan Robertson after Thomas Schelling (1971)

Schelling, perhaps without knowing it, introduced agent-based modelling, where, instead of modelling the system as a whole, the modelling of individual agents enables us to see the emergence of macro-level properties, in this case segregation, via the modelling of micro-level (local) interactions.

We can see the effect of micro-level interactions causing macro-level segregation in the model below (developed by Duncan Robertson after Wilensky after Schelling). Each individual, or agent, decides whether they are unhappy or happy; if they are unhappy, they search until they find a vacant location where they will become happy.  This continues until all individuals attain happiness.

Three Class Segregation Model © Duncan Robertson after Wilensky after Schelling

So, perhaps segregation is not imposed, but is down to us.  Or maybe, in reality, it’s a little bit of both.

Please do get in touch if you would like to discuss building or working with agent-based models.

 

 

The Brexit Paradox: This is not Representative Democracy

In the UK, voters elect a Member of Parliament who is there to represent the views of their constituents.  This is representative democracy, and the UK has survived pretty well with this form of government.  It is one of the many things that the Romans Have Done For Us.

Members of Parliament are supposed to do what their constituents tell them to do.  They may have loyalty to the political party to which they belong, but they should, at least in theory, represent the views of their constituents.

The recent referendum on whether the UK remains a part of, or leaves, the European Union, has caused a great deal of uncertainty, and it is clear, when you think of it, why this is so.

Consider the stylized map of the UK below, where the country is split into three constituencies.  Each constituency has 1 million electors, who all vote.

Constituency A votes 800,000 Leave : 200,000 Remain;
Constituency B votes 400,000 Leave : 600,000 Remain; and
Constituency C votes 400,000 Leave : 600,000 Remain.

This means that there is a total of 800,000 + 400,000 + 400,000 = 1,600,000 voting for Leave; and 200,000 + 600,000 + 600,000 = 1,400,000 voting for Remain.

ReferendumCounting

This is democratic.  The will of the people is that, by a sizeable majority, Leave wins.

However, when this is ratified in Parliament*, by the representatives of the people, the consituents’ MPs, the following happens:

The MP for Consituency A votes Leave;
The MP for Consitutency B votes Remain;
The MP for Consituency C votes Remain.

We are then left in the paradoxical position that a referendum result‡ cannot – under a representative democracy system – be implemented by the MPs.

This is a key constitutional question, and one that cannot be solved by Parliament or the Judiciary†.  This is a fundamental issue for British (and European) democracy.  And its importance cannot be overstated.


* there is a fierce debate on which body needs to invoke Article 50(2) of the Treaty of European Union, but let us assume that Parliament would make this decision ‘in accordance with its own constitutional requirements’ under Article 50(1).
† it is clear that the decision will be the subject of Judicial review, right up to the Supreme court, but this will merely be a judicial rather than a democratic decision.
‡ this is not quite the situation in the actual Brexit referendum result (although there is no way of telling, as MPs’ constituencies are different from referendum counting districts), but the fact remains that the result of a referendum can be inconsistent with implementation under representative democracy.

 

Update 3 November 2016: The High Court (subject to appeal to the Supreme Court) has confirmed that Parliament should decide how to implement withdrawal, as the powers of Royal Perogative would have an impact on Statute, which is not normally the case when treaties are made or revoked.  Brexit is a special case, as it would overturn Statute in a way that was not envisaged in the European Communities Act 1972.  The full judgment is here).