InstantRunoff Voting (IRV) also known as the Alternative Vote (AV), RankedBallot, or RankedChoice voting, is easy. As for other preferential systems it can be done with the exact same ballots as FPTP, and with the exact same singlemember electoral districts; it just needs a change in how we mark the ballots, and how we count them. (And has long and widely been used in Australia state and federal elections as well as in many other places in the world.)
IRV is easy to describe, easy to understand, and easy to count:
 On each ballot the voter just marks the candidates in the order of his or her preference, from 1 meaning most preferred, 2 meaning next preferred, and so on;
 All the ballots are then counted, considering the firstpreference candidates; if this results in a candidate receiving a majority of ballots then that candidate is elected, and we’re done;
 Otherwise we eliminate the candidate having at that point the lowest number of ballots, and reallocate the eliminated candidate’s ballots in terms of their indicated nextpreference choices, and so on, until a majority candidate is determined or all ballot options are exhausted. (With Ranked Pairs we evaluate all preferences holistically without eliminating candidates.)
In the end we get a winner elected on a better majority basis than FPTP, which is desirable.
Note that there is only one voting step, but the reallocation of the votes for eliminated candidates involves multiple counting steps, and requires consideration of all the results from all the polls in order to do this.
It is important to emphasize that under IRV:
 A ballot’s second preference is relevant only if the given ballot’s firstpreference candidate is eliminated. If this secondchoice candidate is not at that point already eliminated the ballot will be allocated to that candidate, otherwise the second preference is ignored, and the ballot’s third preference evaluated, and soon… until the ballot is successfully allocated to a noneliminated candidate, or until all the preferences expressed on the ballot have been exhausted.
 As soon as we get a candidate with a majority we stop, disregarding any further preferences.
 This means that voters’ full expressed preferences do not come into play in the IRV election decision. Lower preferences on any given ballot have no effect at all until or unless all higherpreference candidates on that given ballot have been eliminated, and then only if that lowerpreference candidate is at that point not already eliminated and we have not yet found a majority winner.
There are notable other weaknesses in this system. For example: as for FPTP, “similar” candidates will tend to appeal to the same voter base. Such voters will tend to rate such candidates similarly, which will tend to spread support among them, reducing the individual standings of all such candidates in each round of counting, i.e.: “splitting” the “similar” vote, diminishing the prospects for them all.
This can cause such similar candidates to be eliminated, whereas one of them might otherwise have won.
Unlike FPTP, however, as similar candidates are eliminated their support will tend to be reallocated to the remaining “similar” candidates. If a candidate can survive the count until his or her similar competitors are eliminated, the problem works itself out — at least from the perspective of that surviving candidate!
Consider as well a situation where the firstpreference lastplace candidate though having fewer firstpreference supporters is everyoneelse’s second choice.
Looking at such a strong secondpreference showing one could see, intuitively, that if there is no firstpreference majority this lastplace firstpreference candidate might well be the candidate who in the end is “most preferred” across the board. But, being in last place on the first count he or she would be eliminated straight away.
IRV is sensitive to the order in which candidates are eliminated, which can affect which other candidates are eliminated and in what order.
Ranked Pairs and other Condorcet methods do NOT operate by “eliminating” candidates, and thus are not prey to this fault — all ballot preferences for all valid ballots come into play in determining the outcome.
The following example illustrates how a mostpreferred candidate can be eliminated rather than elected, as well as the case where the leastpreferred candidate is elected rather than eliminated. IRV is NOT a Condorcet method:
1. WinnerLoses Scenario
To demonstrate this let us imagine that we have four candidates: W, X, Y, Z, where W has relatively low firstpreference support, but substantial support after that.
Let us imagine an election by preferrential ballot, where the voters record their preferences among these given candidates by voting 1 for firstpreference, 2 for nextpreference, and so on.
We then evaluate these cases in terms of first past the post (FPTP), Instant Runoff Voting (IRV), and any Condorcet method (there being no preference cycle in these results, a Condorcetcompletion approach is not required).
2. FPTP and IRV Analysis
The following “as voted” table represents all possible permutations (excluding preferredsameas scenarios) of voter preferences, along with vote counts contrived to demonstrate the point at hand:
Preferences: 1  2  3  4  Ballots  

W  6.0%  X  4.0%  Y  Z  2.0% 
Z  Y  2.0%  
Y  0.0%  X  Z  0.0%  
Z  X  0.0%  
Z  2.0%  X  Y  1.0%  
Y  X  1.0%  
X  26.5%  W  21.0%  Y  Z  11.5% 
Z  Y  9.5%  
Y  3.5%  W  Z  2.5%  
Z  W  1.0%  
Z  2.0%  W  Y  1.5%  
Y  W  0.5%  
Y  33.5%  W  20.5%  X  Z  10.5% 
Z  X  10.0%  
X  3.0%  W  Z  5.0%  
Z  W  5.0%  
Z  3.0%  W  X  2.0%  
X  W  1.0%  
Z  34.0%  W  20.0%  X  Y  10.0% 
Y  X  10.0%  
X  10.0%  W  Z  5.0%  
Z  W  5.0%  
Y  4.0%  W  X  2.0%  
X  W  2.0%  
100.0%  100.0%  100.0% 
 By FPTP only the first preference on any ballot is used. Candidate Z, having the most firstpreference ballots, wins — with 34% of the vote.

By IRV, there being no firstpreference majority, we eliminate the lowestscore candidate, W, reallocating his or her ballots according to their nextpreferences, and proceed to the second count:
Candidate W is Eliminated, Ballots reallocated. Voterpreference Ignored, never used.
Upon eliminating candidate W and reallocating his or her ballots according to their nextpreferences, we obtain the secondcount result, as follows:
Preferences: 1  2  3  Ballots  

X  30.5%  Y  Z  17.0% 
Z  Y  13.5%  
Y  33.5%  X  Z  20.5% 
Z  X  13.0%  
Z  36.0%  X  Y  21.0% 
Y  X  15.0%  
100.0%  100.0% 

There still being no majority, we eliminate the lowestscore candidate, X, reallocating his or her ballots according to their nextpreferences, and proceed to the third count:
Candidate X is Eliminated, Ballots reallocated. Voterpreference Ignored, never used.
Upon eliminating candidate X and reallocating his or her ballots according to their nextpreferences, we obtain the third and finalcount result, as follows:
Preferences: 1  2  Ballots 

Y  Z  50.5% 
Z  Y  49.5% 
100.0% 

Having reallocated Candidate X‘s ballots, there is now a majority winner: Candidate Y wins by IRV on the third count.
3. Condorcet Analysis
The Condorcet tally for this scenario looks like this:
Pairs
preferred
than A
Preference
preferred
than B
vs B: [candidate X]
vs B: [candidate Y]
vs B: [candidate Z]
vs B: [candidate Y]
vs B: [candidate Z]
vs B: [candidate Z]
 The winner of each pairwise matchup is shown bold, and there are no preference cycles
 W wins by majority in every pairing in which he or she occurs and is thus the Condorcet winner — by any Condorcet method — and is arguably the candidate “most preferred” by the electorate as a whole.
 Similarly, candidate Z loses every pairing in which he or she occurs, and is thus the Condorcet loser – arguably the candidate “least preferred” by the electorate as a whole.
4. Comparative Results
Note that:
 Candidate W, who wins by any Condorcet method, and is thus arguably the candidate most preferred by the voters, comes in dead last by both FPTP and IRV.
 Candidate Z, who comes in dead last by any Condoret method, and is thus arguably the candidate leastpreferred by the voters, wins by FPTP.
 Candidate Y, who comes in nexttolast by any Condorcet method, wins by IRV.
 Candidate rankings by FPTP vs Condorcet in this case are exactly the reverse of each other!
All systems have their own strengths and weaknesses; some are better than others in different ways, and this is true for preferential voting systems as well; nevertheless, I submit that the worst such preferentialvoting system is still better than FPTP.
IRV isn’t the worst choice, despite its weaknesses. If our choice is only between IRV and FPTP, IRV is a good choice; but we can easily do better.