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Tallying Instant Runoff Voting or Ranked Choice Voting

IRV is complex to count
IRV increases reliance on more complex and bleeding edge technology and requires the central counting of votes.The tallying process used in North Carolina is in direct conflict with North Carolina's statute § 163-182.2.  The use of centraly counting of precinct cast ballots 
opens elections up to the risks of ballot box stuffing or tampering.

Different jurisdictions have adopted different rules and different rules provide different outcomes

Because IRV is so complex, it is quite possible for errors in tabulation to go undiscovered, or if discovered, found only weeks after the fact, as happened in Aspen Colorado.  This was demonstrated in May 2009 in Aspen Colorado when the voting vendor True Ballot used the wrong tallying rules. True Ballot made the mistake of using "Cambridge rules" to tally Aspen's mayoral contest , which caused different results than using the correct rules. When the error was discovered, the election results were re-tallied using the proper formula. You can read more on Burlington's instant runoff voting rules here . The algorithm and instructions for the instant runoff voting tallying software is here at BurlingtonVotes .  

IRV is not additive. There is no such thing as a "subtotal" in IRV. In IRV every single vote may have to be sent individually to the central agency (1,000,000·N numbers, i.e. 1000 times more communication). [Actually there are clever ways to reduce this, but it is still bad.] If the central agency then computes the winner, and then some location sends a correction, that may require redoing almost the whole computation over again. There could easily be 100 such corrections and so you'd have to redo everything 100 times. Combine this scenario with a near-tie and legal and extra-legal battle like in Bush-Gore Florida 2000 over the validity of every vote, and this adds up to a complete nightmare for the election administrators.

The complexity of counting IRV ballots leads to great logistical problems and time-delays as in
San Francisco . IRV counting cannot be started until after all absentee and provisional ballots are judged eligible and are ready to count because any mistake in the first counting round requires that the counting process must be begun all over again. (Imagine recounts of each IRV round in a Minnesota-like recount!) *Thanks to Center for Range Voting for this explanation of IRV tallying.

IRV is not transparent.
Voters have to rely on people instead of an open process. From Voting Matters Blog:
The counting of IRV is complex — the elimination of some candidates at the end of the first round means that second choice votes are transferred to other candidates. If a third round is required the elimination and transfer process continues. The average voter has to place great trust in the reliability of the counting algorithm in a way far beyond what is necessary in plurality voting. So the counting is opaque and non-transparent — a kind of voting voodoo with election officials in the role of witch doctor producing the magical results. If one believes strongly that the average voter should be able to understand and observe the counting of votes in a democracy, then IRV fails to meet this standard.

Tallying Instant runoff voting in NC. Complex, not transparent, error prone
Tallying instant runoff voting in Hendersonville NC: touchscreen nightmare

Tallying instant runoff voting: North Carolina proposed optical scan method. Not easy as 1-2-3
Tallying instant runoff voting in Cary NC in 2007: Manual method. Not easy as 1-2-3

Instant runoff voting - counting by hand a nightmare? tallying IRV in Cary NC in 2007. (Optical Scan Ballots)

It was difficult to count just 3,000 ballots correctly. Officials had to manually tally the IRV results for the Cary, NC “instant runoff”. There was confusion during the counting and ballots were miscounted and not properly allocated to the candidates. Friday, the day after the "runoff" or count of the 2nd round, the election director performed an audit, according to the media. Errors were discovered and the audit extended into a full blown recount...

....According to Chris Telesca who observed the IRV counting in Wake County, NC, to hand-process a little over 3000 paper ballots (after the first choice votes were counted on the op-scan machines) when there were only 3 candidates plus a few write-ins for the Cary district B, single member town council seat, and the counting went only two rounds

it took 6 sorting stacks for each of 12 ballot groupings or precincts (8 precincts plus absentee by mail in Cary, board of elections one-stop site, the Cary one-stop site, provisional ballots- Cary, and possibly some transfer votes from another county which were eligible to vote in the Cary IRV contest) or 12 times 6 stacks = 72 stacks.

Wake County officials decided to put each stack in a separate plastic bag to keep track. This would not be possible if there were more than one IRV contest because each contest requires independent sorting and stacking to count.

The procedure was very complicated, but it was there in print. Even so, the Wake Board of Elections (BOE) didn’t follow it. There was no overhead projector so that observers could follow the process. Non Board members were sorting the ballots into stacks which was hard to follow. Nonetheless, observers and the Board came up with different totals at the end of the day. The next day, the different totals were determined to be caused by a calculator error that was discovered in an “audit” – that also discovered a few missing votes...

Just 3,000 ballots!