What the Indicative Votes Indicate: No Substantive Consensus but Some Meta-Consensus in the House of Commons

Christian List & Kai Spiekermann London School of Economics April 1, 2019

The results of the indicative votes held in the House of Commons on 27 March were greeted with a mixture of disappointment and ridicule. While the lack of a majority for all of the eight options under consideration shows that Parliament is deeply divided about the substantial decisions regarding the future course of the Brexit process, there is a surprising amount of agreement about the structure of the choices ahead. Drawing on tools from social choice theory (the mathematical theory of group decision making), we reveal this structure and show how it indicates possible paths towards a majority. Our main results can be seen in the table below. The table shows a way of arranging groups of MPs on a unidimensional scale, with the green bars indicating the options the dierent groups supported. The most important lessons to take away from the table are:

• Of the 602 MPs that actively supported or opposed at least one option, 511 can be placed on the scale as shown, ranging roughly from No-Deal-Brexit to Ruling-out-No-Deal and/or conducting a second referendum (from left to right in our table). Between these two poles lie several distinct proposals for a close relationship with the EU, involving membership in or alignment with the EU single market and/or a customs union.

• The median group of MPs (indicated in blue) on that scale supports Nick Boles's Common Market 2.0, Ken Clarke's customs union proposal, and the Labour plan for a customs union. This is an indication that one of these proposals (or a mix of them) might nd the support of a majority.

• We can see three possible avenues towards forming alliances among distinct groups. First, it might be possible to convince more supporters of George Eustice's EFTA & EEA proposal to vote for the Boles or Clarke proposals. Second, there is some potential for a compromise position that combines a conrmatory vote (the Beckett proposal) with either Boles, Clarke, or the Labour plan. Third, supporters of the Cherry proposal (revoking Article 50 to avoid no deal) could add support to a position in the centre of our scale.

1 4 Alan Duncan, Mike Freer, Angus Brendan MacNeil, Pete Wishart

Heidi Allen, Hannah Bardell, Luciana Berger, Mhairi Black, Ian Blackford, Kirsty Blackman, Tom Brake, Deidre Brock, Alan Brown, Vince Cable, Lisa Cameron, Alistair Carmichael, Douglas Chapman, Joanna Cherry, Ann Clwyd, Ann Coffey, Ronnie Cowan, Angela Crawley, Edward Davey, Martyn Day, Martin

y Aye Aye Aye Docherty-Hughes, Tim Farron, Marion Fellows, Mike Gapes, Stephen Gethins, Patricia Gibson, Patrick 64 Grady, Peter Grant, Neil Gray, Justine Greening, Dominic Grieve, Drew Hendry, Lady Hermon, Wera Hobhouse, Stewart Hosie, Christine Jardine, Chris Law, Phillip Lee, Chris Leslie, David Linden, Caroline Lucas, Siobhain McDonagh, Stewart Malcolm McDonald, Stuart C. McDonald, Carol Monaghan, Layla Moran, Gavin Newlands, "Brendan OHara", Joan Ryan, Tommy Sheppard, Gavin Shuker, Angela Smith, Owen Smith, Anna Soubry, Chris Stephens, Jo Stevens, Jamie Stone, Jo Swinson, Alison Thewliss, Chuka Umunna, Philippa Whitford, Sarah Wollaston, John Woodcock, Daniel Zeichner

3 David Lammy, Anna McMorrin, Paul Williams Aye Aye Aye

Rosena Allin-Khan, Tonia Antoniazzi, Ben Bradshaw, Lyn Brown, Karen Buck, Ruth Cadbury, Neil Coyle, Mary Creagh, Stella Creasy, Janet Daby, Geraint Davies, Marsha De Cordova, Emma Dent Coad, Stephen Doughty, Rosie Duffield, Maria Eagle, Angela Eagle, Louise Ellman, Chris Elmore, Ruth George, Preet Kaur Gill, Kate Green, Lilian Greenwood, Fabian Hamilton, Helen Hayes, Meg Hillier, Margaret Hodge, Rupa Huq, Darren Jones, Susan Elan Jones, Liz Kendall, Ged Killen, Clive Lewis, Rachael Maskell, Christian Matheson, Kerry McCarthy, Catherine McKinnell, Madeleine Moon, Stephen Morgan, Kate Osamor, Ellie Reeves, Lloyd Russell-Moyle, Barry Sheerman, Tulip Siddiq, Andy Slaughter, Wes Streeting, Anna Turley, Thelma Walker, Catherine West, Martin Whitfield

Rushanara Ali, Clive Betts, Roberta Blackman-Woods, Paul Blomfield, Kevin Brennan, Bambos Charalambous, David Crausby, Alex Cunningham, Thangam Debbonaire, Anneliese Dodds, David Drew, Clive Efford, Bill Esterson, Paul Farrelly, Vicky Foxcroft, James Frith, Hugh Gaffney, Roger y Aye Aye Godsiff, John Grogan, Louise Haigh, Harriet Harman, George Howarth, Sarah Jones, Peter Kyle, Lesley Laird, Shabana Mahmood, Sandy Martin, Chi Onwurah, Albert Owen, Matthew Pennycook, Jess Phillips, Luke Pollard, Faisal Rashid, Steve Reed, Rachel Reeves, Marie Rimmer, Matt Rodda, Danielle Rowley, Virendra Sharma, Jeff Smith, Karin Smyth, Alex Sobel, Paul Sweeney, Gareth Thomas, Stephen Timms, Stephen Twigg, Keith Vaz, Matt Western, Alan Whitehead, Mohammad Yasin

Diane Abbott, Mike Amesbury, Jonathan Ashworth, Adrian Bailey, Hilary Benn, Nicholas Brown, Chris Bryant, Richard Burden, Richard Burgon, Liam Byrne, Dan Carden, Jenny Chapman, Vernon Coaker, Yvette Cooper, Jeremy Corbyn, John Cryer, Wayne David, Tanmanjeet Singh Dhesi, Peter Dowd, Jack Dromey, Colleen Fletcher, Gill Furniss, Helen Goodman, Nia Griffith, David Hanson, Emma Hardy, Sue

y y Aye Aye Aye Hayman, Sharon Hodgson, Kate Hollern, Imran Hussain, Diana Johnson, Gerald Jones, Afzal Khan, Tony Lloyd, Rebecca Long Bailey, Ian C. Lucas, Holly Lynch, Khalid Mahmood, Seema Malhotra, Gordon Marsden, Steve McCabe, Andy McDonald, John McDonnell, Conor McGinn, Edward Miliband, Alex Norris, Toby Perkins, Laura Pidcock, Stephen Pound, Lucy Powell, Yasmin Qureshi, Angela Rayner, Christina Rees, Emma Reynolds, Jonathan Reynolds, Geoffrey Robinson, Chris Ruane, Naz Shah, Cat Smith, Eleanor Smith, Keir Starmer, Emily Thornberry, Karl Turner, Liz Twist, Valerie Vaz, Tom Watson, Phil Wilson

Ian Austin, Tracy Brabin, Julie Cooper, Jon Cruddas, Gloria De Piero, Chris Evans, Mary Glindon, Andrew Gwynne, Carolyn Harris, Dan Jarvis, Helen Jones, Mike Kane, Ivan Lewis, Justin Madders, Liz y y y Aye Aye Aye Aye Aye Aye Aye Aye Aye Aye Aye

26 050 50 67 22 McInnes, Jim McMahon, Ian Mearns, Melanie Onn, Stephanie Peacock, Jo Platt, Paula Sherriff, Jon Trickett Median

4 Richard Benyon, Vicky Ford, Margot James, Nicholas Soames Aye Aye

Nick Boles, Steve Brine, Alistair Burt, Stephen Crabb, Jonathan Djanogly, George Freeman, Nick

Aye Herbert, Simon Hoare, Jeremy Lefroy, Oliver Letwin, Paul Masterton, Nicky Morgan, Robert Neill, Mark Pawsey, Caroline Spelman, Edward Vaizey

Bim Afolami, James Cartlidge, Damian Collins, Alberto Costa, Robert Halfon, Simon Hart, Kevin y Aye Aye Hollinrake, Rebecca Pow, John Stevenson, David Tredinnick

y y Aye Aye Aye Peter Aldous, David Duguid, Luke Graham, Bill Grant, Stephen Kerr, Mark Prisk, Gary Streeter

Nigel Adams, Kemi Badenoch, Gregory Campbell, Nigel Dodds, Jeffrey M. Donaldson, Michelle Donelan, Philip Dunne, Paul Girvan, George Hollingbery, Alister Jack, Pauline Latham, Emma Little Pengelly, Ian Paisley, Chris Philp, Gavin Robinson, Jim Shannon, David Simpson, Graham Stringer, Theresa Villiers, Sammy Wilson

Adam Afriyie, David Amess, Stuart Andrew, Richard Bacon, Steve Baker, Henry Bellingham, Crispin Blunt, Peter Bone, Ben Bradley, Suella Braverman, Jack Brereton, Andrew Bridgen, Fiona Bruce, Conor Burns, William Cash, Christopher Chope, Simon Clarke, Geoffrey Clifton-Brown, David T. C. Davies, Philip Davies, Caroline Dinenage, Nadine Dorries, Steve Double, Richard Drax, James Duddridge, Iain Duncan Smith, Charlie Elphicke, Nigel Evans, Michael Fabricant, Mark Francois, Marcus Fysh, Zac

Unidimensional Votes Indicative of Ordering Goldsmith, James Gray, Chris Green, Mark Harper, Rebecca Harris, John Hayes, Kate Hoey, Philip y Aye Aye Hollobone, Adam Holloway, Eddie Hughes, Ranil Jayawardena, Bernard Jenkin, Andrea Jenkyns, Boris Johnson, Caroline Johnson, Gareth Johnson, David Jones, Mark Lancaster, Edward Leigh, Andrew Lewer, Julian Lewis, Julia Lopez, Jonathan Lord, Tim Loughton, Craig Mackinlay, Rachel Maclean, Anne Main, Alan Mak, Kit Malthouse, Paul Maynard, Stephen McPartland, Esther McVey, Stephen Metcalfe, Maria Miller, Nigel Mills, Sheryll Murray, Matthew Offord, Priti Patel, Owen Paterson, Christopher Pincher, Tom Pursglove, Will Quince, Dominic Raab, Jacob Rees-Mogg, Laurence Robertson, Andrew Rosindell, Lee Rowley, Paul Scully, Grant Shapps, Henry Smith, Royston Smith, Andrew Stephenson, Bob Stewart, Iain Stewart, Graham Stuart, Rishi Sunak, Desmond Swayne, Ross Thomson, Justin Tomlinson, Michael Tomlinson, Anne-Marie Trevelyan, Shailesh Vara, Giles Watling, Helen Whately, Heather Wheeler, John Whittingdale, Bill Wiggin, William Wragg

John Baron, Jake Berry, Rehman Chishti, Tracey Crouch, Mims Davies, David Davis, Jackie Doyle-Price, Michael Ellis, Nusrat Ghani, Robert Goodwill, Andrew Griffiths, Chris Heaton-Harris, Robert Jenrick, Marcus Jones, Daniel Kawczynski, Greg Knight, Kwasi Kwarteng, Ian Liddell-Grainger, Jack Lopresti, y Aye Aye Mark Menzies, Johnny Mercer, Amanda Milling, Anne Marie Morris, James Morris, Wendy Morton, Andrew Murrison, "Neil OBrien", Mike Penning, Mark Pritchard, John Redwood, Bob Seely, Mark Spencer, Robert Syms, Maggie Throup, Kelly Tolhurst, Craig Tracey, Martin Vickers, Matt Warman, Craig Whittaker, Mike Wood

Edward Argar, Victoria Atkins, Harriett Baldwin, Paul Beresford, Peter Bottomley, Andrew Bowie, Graham Brady, Robert Buckland, Alex Burghart, Jo Churchill, Colin Clark, James Cleverly, Th?r?se Coffey, Oliver Dowden, David Evennett, Frank Field, Lucy Frazer, Roger Gale, Nick Gibb, Cheryl Gillan, John Glen, Richard Graham, Helen Grant, Kirstene Hair, Luke Hall, Greg Hands, James Heappey, Peter Heaton-Jones, Stephen Hepburn, John Howell, Nigel Huddleston, Nick Hurd, Andrew Jones, Gillian 54 92 016 10 7 20 99 40 55 Keegan, Seema Kennedy, John Lamont, Patrick McLoughlin, Damien Moore, David Morris, Jesse Norman, Guy Opperman, Jeremy Quin, Mary Robinson, Douglas Ross, Andrew Selous, Alok Sharma, Keith Simpson, Chris Skidmore, Chloe Smith, Mel Stride, Hugo Swire, Tom Tugendhat, Charles Walker, Robin Walker, Nadhim Zahawi Votes inVotes Group Baron: Deal No Eustice: Efta & Eustice: EEA Efta Corbyn: Labour's Plan Corbyn: Labour's Clarke: Customs Union Fysh: Managed No Deal No Fysh: Managed Boles: CommonMarket 2.0 Cherry: Deal ToRevoke Avoid No Beckett: Confirmatory PublicVote We now briey explain our analysis in more detail. (We provide a companion document with more technical information and references on our websites.) The options selected by speaker Bercow for indicative votes were:

• Baron: No Deal

• Fysh: Managed No Deal

• Eustice: Efta and EEA

• Boles: Common Market 2.0

• Clarke: Customs union

• Corbyn: Labour's plan

• Beckett: Conrmatory public vote

• Cherry: Revoke to avoid No Deal MPs were able to cast votes on all these options. Rather than ranking the options in an order of preference, MPs were asked to vote for as many or as few options as they liked. For each option, they could indicate their approval or disapproval (with abstention allowed). Thus, they were asked to cast what social choice theorists call approval ballots. In this context, a vote for any given option is best interpreted as expressing an opinion to the eect that this option is in principle acceptable (even if it may not be the relevant MP's most preferred option). 602 MPs had at least one Aye or No on their ballot paper. We excluded all MPs who abstained throughout (this includes the cabinet and most government ministers who followed an instruction to abstain). We then looked for a way to order the MPs based on the votes they cast. Social choice theory suggests the criterion of unidimensional ordering. Informally, the idea is to order MPs on a single dimension (or scale) such that, for each option, the MPs supporting that option form a connected block. These blocks are shown as green bars in the table. One can see that there is only one connected green bar for each option, as demanded by unidimensional ordering. One core advantage of our approach is that voting patterns become visible on an intuitive scale and therefore easier to interpret. We can think of unidimensional ordering as corresponding to a kind of meta-consensus: a consensus, not on which option to approve, but rather on an underlying normative or cognitive dimension that structures the disagreement between the voters. Several dierent interpretations of the ordering based on the indicative votes are possible. We think that a plausible interpretation takes the scale as ranging from Support-for-No-Deal to Oppose-No-Deal and/or Support- New-Referendum. As with any tool for simplifying complicated results, there is a cost: the voting patterns of 91 MPs do not t into our scale. (The companion document lists these MPs and their voting patterns.) There are a variety of reasons for that: some had a less common voting pattern (e.g., supporting Clarke, Corbyn and Beckett, but not Cherry), some only supported one option, others supported an unusually wide range of options. The point of our analysis is not that these votes are less important or less considered, it only suggests that they resist the simplication we propose. It might also be worth noting that a remarkable 56 MPs in that group of 91 MPs supported the Clarke proposal, giving it relatively more support than suggested by our table. To sum up, the fact that 511 of 602 MPs are included in a form of meta-consensus suggests that the views of MPs have more structure than one might initially expect: they largely agree on which proposals are similar or distant in a one-dimensional political landscape, and they position themselves in that landscape. The upshot is that attempts to form a majority could draw on this meta-consensus about the landscape we identied. Our analysis should make it easier for MPs and the wider public to

3 understand current sources of substantial disagreement and why the indicative votes did not produce a majority the rst-time round. It might further help to turn meta-consensus into a stable majority position in the next round of indicative votes. But our analysis also reminds us that success requires a compromise position that nds support in more than half of the political landscape.

Biographical Information Christian List is Professor of Philosophy and Political Science in the Department of Philosophy, Logic and Scientic Method at the London School of Economics. He works in individual and social choice theory, the theory of democracy, and a number of areas in and around the philosophy of science and social science. In 2011, he published Group Agency: The Possibility, Design, and Status of Corporate Agents (with Philip Pettit). His latest book is Why Free Will is Real (to appear this spring). You can nd more information about him at: http://personal.lse.ac.uk/LIST Kai Spiekermann is Associate Professor of Political Philosophy in the Department of Government at the London School of Economics. He works in democratic theory and the philosophy of the social sciences. Among his research interests are group decisions, social epistemology (and especially epistemic justications of democracy), the ethics of environmental change, and the methodology of political theory and political science. His latest book is An Epistemic Theory of Democracy (with Robert E. Goodin). You can nd more information about him at: http://www.kaispiekermann.net

4