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What’s The Best Campaign Route In The 2015 U.K. General Election?

What do political campaigning and a famous math problem have in common? Plenty — if you’re deciding where to send your party leader out campaigning.

Between now and May 7, the political parties running in this year’s British general election will have to decide where to send their party campaign buses and their party leaders. The BBC has been tracking where they’ve gone so far — but where, ideally, should their battle buses go next?

Because Britain is fairly small compared to the U.S. (“slightly smaller than Oregon,” as the CIA puts it), traveling by bus is a reasonable way to get around the country. Trains and planes are fine too — but occasionally risky.

But a campaign bus — even one with tasteful accoutrements — is only useful if you know where to send it.

That’s where math comes in. If party leaders have to visit, say, 40 constituencies, how do they know the best order in which to visit them?1 The total number of possible orderings of constituencies is vast — not numbers of atoms in the universe vast, but large enough to make it awkward to figure out which order will produce the shortest itinerary

Thankfully, given that this problem — also called the traveling salesman problem — is fairly well known, there are a number of helpful algorithms for finding the optimal route, or a route that’s as close to optimal as makes no difference.

Armed with these algorithms — and some handy code from Randal Olson for calculating travel times using Google — we worked out the best route for each party through 40 seats that could tip the balance — 20 just below our forecast seat total for each party, and 20 just above.2

Along these routes, the parties will have to fight different opponents: for David Cameron’s Conservative party, that might be Labour in some seats but the Liberal Democrats in others.

In practice, party leaders won’t follow our routes. David Cameron, Ed Miliband and Nick Clegg all have media engagements that require them to head back to London from time to time. Party strategists will also realize that some trips to marginal but remote constituencies (Hello, Caithness!) simply take up too much time. But these routes are a good indication of how geographically spread out parties’ campaigning efforts need to be this year.

Conservatives

David Cameron’s journey starts in the border area of Scotland, where the Conservatives could pick up two seats and take the edge off their unpopularity in Scotland. From there, it’s down south to circle around Manchester and Liverpool. The party then heads southwest into the Midlands before taking two large detours northeast (to Cleethorpes) and east (Norwich North). After heading through London and taking in some of the towns along the coast, the Conservative campaign makes a brief detour into Wales before ending its trip in the South West with a visit to Land’s End (St Ives). A list of the constituencies to visit and the time it takes to travel between them is in the footnotes.3

Conservatives_map

Total time in transit: 1 day, 16 hours, 22 minutes.

Labour

Ed Miliband starts in Wales, in seats he and the Labour party hope to keep from Plaid Cymru. After moving down into South Wales, the Labour campaign moves on to some Midlands seats before getting its London visit in early. It’s then on to Brighton, to fight both the Greens and the Conservatives, before moving up the coast to Norwich North and Cleethorpes — two seats that also featured in the Conservatives’ list. Labour then heads through Sheffield and Manchester before crossing over into Scotland and working its way along the central belt and up the coast, finishing in Aberdeen.4

Labour_map

Total time in transit: 1 day, 14 hours, 22 minutes

Liberal Democrats

Nick Clegg and the Liberal Democrats begin their journey on to the windswept North Norfolk coast before heading into London. With a brief detour to Cheltenham, they trace the outline of the coast, heading to St Ives before following the Severn Estuary up into Wales. The party then zigzags through the North of England before getting to a number of Scottish seats it must defend — even at the cost of long and tiring journeys through the Highlands.5

Liberal Democrats_map

Total time in transit: 1 day, 23 hours, 55 minutes.

The Liberal Democrats have the longest total time in transit — meaning that if the prospect of losing more than half their seats weren’t enough, they’ll also have to put up with fighting in geographically dispersed locations.

This long tour reflects the Liberal Democrats’ awkward position within the party system: They fight Conservatives in some rural parts of the country and Labour in some urban areas. That means their target seats are widely dispersed. Better hope those campaign buses have toilets on them.

What’s the benefit?

In their campaign activities, parties face really complex optimisation problems. What’s the marginal return on an extra campaign stop versus more time spent with local journalists? Is it better to leave local campaigners in rural constituencies to their own devices? But getting the right answers to these questions matters. Research has shown that visits by popular leaders can boost a party’s vote share by a percentage point. In an election this close, that’s too many votes to leave on the table.

Check out our 2015 general election predictions and full U.K. election coverage.

Footnotes

  1. There’s no special reason for choosing 40 constituencies to do this analysis, but plotting more than that runs into limits on the Google Distance API that we’re using here.

  2. For each party, we ranked constituencies according to the party’s probability of victory, and took constituencies from (n-20) to (n+20), where n is the number of constituencies we predicted that party to win in our March 30 forecast. Thus, for the Liberal Democrats (forecast to win 25 seats on March 30), we looked at their fifth through 45th seats. To calculate the “center” of each constituency, we used information on the latitude and longitude of census tracts. These census tracts have roughly similar populations, so by taking the median latitude and longitude, we get a good approximation of the population-weighted centroid of each constituency.

    1. Berwickshire, Roxburgh and Selkirk to Dumfries and Galloway (~128 minutes)
    2. Dumfries and Galloway to Morecambe and Lunesdale (~128 minutes)
    3. Morecambe and Lunesdale to Blackpool North and Cleveleys (~48 minutes)
    4. Blackpool North and Cleveleys to South Ribble (~41 minutes)
    5. South Ribble to Pendle (~34 minutes)
    6. Pendle to Bury North (~33 minutes)
    7. Bury North to Pudsey (~55 minutes)
    8. Pudsey to Calder Valley (~34 minutes)
    9. Calder Valley to Colne Valley (~20 minutes)
    10. Colne Valley to High Peak (~51 minutes)
    11. High Peak to Cheadle (~39 minutes)
    12. Cheadle to Warrington South (~31 minutes)
    13. Warrington South to Wirral West (~37 minutes)
    14. Wirral West to Dudley South (~117 minutes)
    15. Dudley South to Halesowen and Rowley Regis (~15 minutes)
    16. Halesowen and Rowley Regis to Cannock Chase (~33 minutes)
    17. Cannock Chase to Amber Valley (~56 minutes)
    18. Amber Valley to Loughborough (~34 minutes)
    19. Loughborough to Nuneaton (~41 minutes)
    20. Nuneaton to Northampton North (~55 minutes)
    21. Northampton North to Cleethorpes (~153 minutes)
    22. Cleethorpes to Norwich North (~174 minutes)
    23. Norwich North to Ipswich (~76 minutes)
    24. Ipswich to Clacton (~43 minutes)
    25. Clacton to Enfield North (~82 minutes)
    26. Enfield North to Finchley and Golders Green (~22 minutes)
    27. Finchley and Golders Green to Ealing Central and Acton (~19 minutes)
    28. Ealing Central and Acton to Harrow East (~22 minutes)
    29. Harrow East to Ilford North (~38 minutes)
    30. Ilford North to Croydon Central (~50 minutes)
    31. Croydon Central to Hastings and Rye (~80 minutes)
    32. Hastings and Rye to Brighton, Kemptown (~63 minutes)
    33. Brighton, Kemptown to Hove (~14 minutes)
    34. Hove to Southampton, Itchen (~78 minutes)
    35. Southampton, Itchen to Bath (~101 minutes)
    36. Bath to Bristol North West (~36 minutes)
    37. Bristol North West to Brecon and Radnorshire (~99 minutes)
    38. Brecon and Radnorshire to Torbay (~182 minutes)
    39. Torbay to North Cornwall (~91 minutes)
    40. North Cornwall to St Ives (~71 minutes)

    1. Ynys Mon to Arfon (~31 minutes)
    2. Arfon to Carmarthen East and Dinefwr (~209 minutes)
    3. Carmarthen East and Dinefwr to Bristol North West (~99 minutes)
    4. Bristol North West to Halesowen and Rowley Regis (~84 minutes)
    5. Halesowen and Rowley Regis to Dudley South (~15 minutes)
    6. Dudley South to Cannock Chase (~40 minutes)
    7. Cannock Chase to Birmingham, Yardley (~35 minutes)
    8. Birmingham, Yardley to Nuneaton (~30 minutes)
    9. Nuneaton to Loughborough (~41 minutes)
    10. Loughborough to Harrow East (~107 minutes)
    11. Harrow East to Ealing Central and Acton (~22 minutes)
    12. Ealing Central and Acton to Finchley and Golders Green (~19 minutes)
    13. Finchley and Golders Green to Ilford North (~22 minutes)
    14. Ilford North to Croydon Central (~50 minutes)
    15. Croydon Central to Hove (~58 minutes)
    16. Hove to Brighton, Kemptown (~14 minutes)
    17. Brighton, Kemptown to Hastings and Rye (~63 minutes)
    18. Hastings and Rye to Ipswich (~142 minutes)
    19. Ipswich to Norwich North (~76 minutes)
    20. Norwich North to Cleethorpes (~174 minutes)
    21. Cleethorpes to Leeds North West (~93 minutes)
    22. Leeds North West to Pudsey (~11 minutes)
    23. Pudsey to Colne Valley (~36 minutes)
    24. Colne Valley to Calder Valley (~20 minutes)
    25. Calder Valley to Pendle (~50 minutes)
    26. Pendle to South Ribble (~34 minutes)
    27. South Ribble to Blackpool North and Cleveleys (~41 minutes)
    28. Blackpool North and Cleveleys to Dumfries and Galloway (~155 minutes)
    29. Dumfries and Galloway to Central Ayrshire (~99 minutes)
    30. Central Ayrshire to Paisley and Renfrewshire North (~40 minutes)
    31. Paisley and Renfrewshire North to Glasgow North West (~15 minutes)
    32. Glasgow North West to Motherwell and Wishaw (~31 minutes)
    33. Motherwell and Wishaw to Airdrie and Shotts (~14 minutes)
    34. Airdrie and Shotts to East Lothian (~49 minutes)
    35. East Lothian to Edinburgh South (~24 minutes)
    36. Edinburgh South to Edinburgh North and Leith (~14 minutes)
    37. Edinburgh North and Leith to Kirkcaldy and Cowdenbeath (~38 minutes)
    38. Kirkcaldy and Cowdenbeath to Glenrothes (~14 minutes)
    39. Glenrothes to Aberdeen South (~105 minutes)
    40. Aberdeen South to Aberdeen North (~10minutes)

    1. North Norfolk to South East Cambridgeshire (~103 minutes)
    2. South East Cambridgeshire to Cambridge (~22 minutes)
    3. Cambridge to St. Albans (~61 minutes)
    4. St. Albans to Watford (~18 minutes)
    5. Watford to Hornsey and Wood Green (~29 minutes)
    6. Hornsey and Wood Green to Bermondsey and Old Southwark (~27 minutes)
    7. Bermondsey and Old Southwark to Twickenham (~39 minutes)
    8. Twickenham to Kingston and Surbiton (~15 minutes)
    9. Kingston and Surbiton to Sutton and Cheam (~18 minutes)
    10. Sutton and Cheam to Lewes (~67 minutes)
    11. Lewes to Portsmouth South (~79 minutes)
    12. Portsmouth South to Eastleigh (~25 minutes)
    13. Eastleigh to Winchester (~24 minutes)
    14. Winchester to Cheltenham (~89 minutes)
    15. Cheltenham to Bristol West (~48 minutes)
    16. Bristol West to Bath (~32 minutes)
    17. Bath to Yeovil (~68 minutes)
    18. Yeovil to Torbay (~84 minutes)
    19. Torbay to St. Austell and Newquay (~104 minutes)
    20. St. Austell and Newquay to St. Ives (~56 minutes)
    21. St. Ives to North Cornwall (~71 minutes)
    22. North Cornwall to North Devon (~75 minutes)
    23. North Devon to Taunton Deane (~61 minutes)
    24. Taunton Deane to Brecon and Radnorshire (~133 minutes)
    25. Brecon and Radnorshire to Ceredigion (~106 minutes)
    26. Ceredigion to Montgomeryshire (~111 minutes)
    27. Montgomeryshire to Birmingham, Yardley (~104 minutes)
    28. Birmingham, Yardley to Southport (~127 minutes)
    29. Southport to Cheadle (~64 minutes)
    30. Cheadle to Hazel Grove (~17 minutes)
    31. Hazel Grove to Sheffield, Hallam (~56 minutes)
    32. Sheffield, Hallam to Leeds North West (~63 minutes)
    33. Leeds North West to Berwick-upon-Tweed (~147 minutes)
    34. Berwick-upon-Tweed to Berwickshire, Roxburgh and Selkirk (~84 minutes)
    35. Berwickshire, Roxburgh and Selkirk to Edinburgh West (~62 minutes)
    36. Edinburgh West to North East Fife (~60minutes)
    37. North East Fife to Gordon (~120 minutes)
    38. Gordon to Caithness, Sutherland and Easter Ross (~218 minutes)
    39. Caithness, Sutherland and Easter Ross to Ross, Skye and Lochaber (~175 minutes)

Chris Hanretty is reader in politics at the University of East Anglia.

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