Extra cost to count an AV election: £1.3m nationally per election
Extra cost to educate: Potentially an extra £2m per election year at most (£8m over 4 years).
Extra cost to run this referendum: Cost of referendum is seen as the same cost as an election, so
Extra voter education on referendum: As above, an extra £4m at most spanning two financial years. Edit: It turns out that No2AV aren't specifically talking about just voter education for this referendum, so I'll use the Electoral Commissions £9m estimate as the No side have.
This works out at a total yearly cost, over the course of 4 years until the next election is complete, would be
A long cry from "£250m unless you vote no"!
Not that any of this really matters, the cost implication, when such small amounts of money (in the national sense), being discussed with relation to increasing democratic integrity of our voting system is a perverse discussion to have anyway. But referendum aside, are we really going to get angry over an absolute maximum of about 4p per year per person to have a more inclusive, honest, transparent and ultimately fairer system for the individual voter?
But anyway, how to work this out? You can do it for yourself if you like...
First of all, the referendum. This is a cost that will be incurred regardless of the result. You can argue all you like about how much the cost is too much, but it is going to happen. The question is whether you engage with it or not, if you do then voting No will not make the referendum itself cheaper.
The cost of the referendum has been estimated in the House of Commons at £82m. This, I feel, is an under estimate of the total cost of a stand-alone referendum. The Ministry for Justice (who pay out for election costs) paid around £90m for the last european elections. The count was more complicated, but turnout was lower, than FPTP. I'd prefer to use this value as it won't under-value the cost.
However this referendum won' be stand-alone, it will be held along side our local elections (and others in Scotland). When assessing this in 1999 the presumption was that a referendum would cost £50m if standalone, but that only £30m would be extra cost above another poll. As such I think it is only reasonable to assume similarly that the referendum's true cost is more likely to be £54m, 60% of the stand-alone cost. This is because costs such as security, building hire, postage, overseers and more can be shared across the multiple elections, while time taken to count and cost of printing materials cannot.
EDIT: New information from parliament shows that the estimate for the cost of the 2010 election stands at around £110m, up from the cost of the 2005 election. With a few more seats, a greater turnout, and inflation this all seems to be about right. As such the cost is likely to be up from the £54m I state above, to £66m
Referendum cost difference to No 2 AV estimate:
Then there is the need for some voter education on the referendum. No2AV have this at £9m, though I am unsure of where they are getting this figure from. The reason I say this is that it is the Electoral Commission who have the responsibility for raising voter awareness as an arm of the state. Other organisations and groups can no doubt do what they wish as well, and do, but in terms of public funding the Electoral Commission is the only body that receives our money to educate people about elections and registering to vote.
It's important to know that the Electoral Commission is bound by the Political Parties, Elections and Referendums Act 2000, where under Section 13(1) it is made clear their responsibility is to raise awareness for voting systems in the UK.
(1)The Commission shall promote public awareness of—
(a)current electoral systems in the United Kingdom and any pending such systems, together with such matters connected with any such existing or pending systems as the Commission may determine;
(b)current systems of local government and national government in the United Kingdom and any pending such systems; and
(c)the institutions of the European Union.
(4)The Commission shall perform their functions under subsection (1) in such manner as they think fit but may, in particular, do so by—
(a)carrying out programmes of education or information to promote public awareness of any of the matters mentioned in subsection (1); or
(b)making grants to other persons or bodies for the purpose of enabling them to carry out such programmes.
This is all well and good, but it is regulated in how much it can spend each financial year on these purposes by a statutory instrument, The Electoral Commission (Limit on Public Awareness Expenditure) Order 2002. This puts a block of £7.5m per year on spending for awareness, which includes voter education. For them to spend £9m they would have to be spending some money from this current financial year and a significant amount of the next financial year's allowance too.
The money for voter awareness clearly spans in to many areas, such as registering to vote, how the voting systems work, etc. As such it is also money required for general use in other elections too, such as our local elections and the General Election just past. I feel I'm being very liberal in my allocation of money to the AV referendum by saying that £5.5m of the yearly allowance is certain to be already spent on the last set of General and Local elections, which only leaves £2m left to actually use this year. That's if it gets used of course, and next year the likelihood is that another £5.5m will be certainly used on voter awareness even if the AV referendum wasn't taking place.
Take a look at the Electoral Commission's reports for yourself, in 2009-2010 they only spent this £5.5m, while in other years (such as the General Election year in 2005, and a year with only local elections in 2006) they spent more than this. It is unfeasible that, even taking in to account the two years as a source of funding that they could use, more than £4m could be spent on education for the AV referendum.
EDIT: It turns out that the No camp aren't talking purely about voter awareness when they talk about this figure, but the wider costs of the Electoral Commission running the referendum. It is debatable as to whether this cost is included in the costs that are given in Parliament for each election, however for the sake of continuing a worse case scenario I'm assuming it is not. £9m is what the Electoral Commission say it'll cost them in this referendum, so that's what we'll go with.
Referendum education cost difference to No 2 AV estimate:
That brings us now on to the cost of the actual voting system and it's use every 5 years.
First up, we can discount No 2 Av's £130m estimate of costs for voting machines straight away. They aren't necessary (and I'll hopefully show you why they're not necessary in my workings next, it's pretty damn obvious why they're surplus to requirements), they aren't used in places like Australia that have counted their results by hand for almost a century. There is no proof even that it is likely that electronic voting machines will be used, as Channel 4's Fact Check revealed today.
But how about the extra time and money to count by hand?
In Bristol there were 929 staff in 2010, therefore likely around 150 counting staff for Bristol North West, of which about half would be doing the real counting (my old constituency, and a three way marginal in all but name before the election) as one of four constituencies in the city. The average rate to count for staff involved is 150 ballots per hour with 50336 ballots to count for the General Election; they should therefore complete the total count for the general election alone in around 4 hours (though administration may mean this is less efficient, and rechecks or close counts may also increase times).
Further facts: Bristol North West had 36 polling stations, an electorate of around 73500 people, a turnout of 50336, and I'm assuming 6750 postal votes were cast (out of a therefore assumed 9000 total registered based on Ministry of Justice basis for cost calculations) based on an equal share of 27000 in all of Bristol.
The cost of administering Bristol North West would have been estimated using Justice Ministry figures at around £97.5k + the returning officer's fee (around £2500).
In Bristol North West about 30% of the ballots might have had to be recounted (a high figure given the three way marginal nature of the seat, and certainly not as likely in most other constituencies where recounts would be needed), or no more than 130 hours worth of counting staff's time (19500 votes cumulatively, recounted at 150 per hour). This is a maximum because counting techniques that bunch people's next preference together can reduce the time needed to count by "block" counting a shift in votes, and the additional time assumes that people vote in such a way that the maximum number of redistributions need to take place.
But even with a worse case scenario here that is at most (assuming some counting staff aren't used, or my counting staff estimate is too high) an extra cost of less than £2200, or 2.2% extra cost incurred of the whole of constituency cost of election (19.96% of the FPTP counting cost).
This would be replicated across all but a third of the constituencies (most likely, due to those MPs already sitting on 50% wins), to bring that percentage increase down to about 1.2% across all constituencies for the general election.
Therefore, if an election costs around £90mil due to administration and postage costs, then introducing AV will cost about an extra £1.3m depending on the level of involvement of London constituencies. As far as time goes it would appear that the transfer of votes could be calculated to take no more than three hours extra, so a far cry from the "days" some wish to claim, and within the timeframe that long FPTP counts would be completed by.
Vote counting cost difference to No 2 AV estimate: -£128.7m
Next, the cost of voter education. As above the same rules apply to the Electoral Commission on education for elections. £7.5m max. The idea that the country could spend £26m extra on voter education is impossible under current law, as it would be a cost of £5.2m per year to achieve that, and we already know that the maximum that can be improved on is £2m a year! At worst the cost of education for voters (which if it occurs, would clearly be necessary to ensure people feel informed about their elections!) would be £8m.
Of course realistically we're more likely looking at only £1m-2m in one year, but I'm trying to paint a worse case scenario here, within reason and current law.
Voting education cost difference to No 2 AV estimate: -£18m
So in total the amount that No 2 AV seem to have over-estimated their possibilities is to the tune of £180m (£190m due to their habit of rounding up).
It'd be nice if the No camp could provide equally thought out costings to prove their side (though it seems evident that it would be impossible), but even where I have asked those like Charlotte Vere and other prominent supporters and campaigners for the No camp they have declined to answer my requests.
 Returning officers expenses accounts for 2009-10: http://www.official-documents.gov.uk/document/hc1011/hc05/0550/0550.pdf
(2009's european elections, more up to date than the estimates based on 2005 election)
 Referendum held on same day as other election is cheaper: http://www.ucl.ac.uk/spp/publications/unit-publications/34.pdf
 The law for electoral commission: http://www.legislation.gov.uk/ukpga/2000/41/section/13
 Statutory instrument capping spending at £7.5m : http://www.legislation.gov.uk/uksi/2002/505/article/2/made
 Electoral commission annual report 2009-2010: http://www.electoralcommission.org.uk/__data/assets/pdf_file/0012/100722/Resource-Accounts-2009-10.pdf
 Electoral commission annual report 2005-2006: http://www.electoralcommission.org.uk/__data/assets/pdf_file/0008/78182/annulaccounts0506.pdf
 Electoral commission annual report 2006-2007: http://www.electoralcommission.org.uk/__data/assets/pdf_file/0010/56269/Annual-Accounts-Final-Web-Optimised.pdf
 Factcheck The AV campaign gets dirty: http://blogs.channel4.com/factcheck/factcheck-the-av-campaign-gets-dirty/5789
 Bristol north west: http://en.wikipedia.org/wiki/Bristol_North_West_(UK_Parliament_constituency)
 Postal votes numbers for Bristol: http://www.bristol.gov.uk/committee/2010/wa/wa041/0727_6.pdf
 Cost of running an election in a constituency: http://www.justice.gov.uk/guidance/docs/ro-expense-guidance1.pdf