On the eve of his party's spring assembly in Southport this weekend, the Liberal Democrat leader said: "Two years ago we were the third party of government at the local level in this country; now we're the second party."
But Mr Ashdown then added in an interview with the BBC Radio 4's Today programme that although the electoral system remained the same, "we shall change it at national level in the next three or four years, which will make our chances of growth and progress even better".
Given the size of the Government's majority, it is likely that Tony Blair will go for his full, five-year term before he calls an election in 2002 - in which case Mr Ashdown appears to expect to have a new voting system in place for that poll.
But Labour's manifesto only promises a referendum - not enactment. It says: "We are committed to a referendum on the voting system for the House of Commons.
"An independent commission on voting systems will be appointed early to recommend a proportional alternative to the first-past-the-post system."
That commission has already been set up, under the chairmanship of Lord Jenkins of Hillhead, the former Labour Chancellor and ex-leader of the Social Democratic Party, and is due to report later this year, but there has been no public commitment to early legislation.
Ten years after the Liberal Party and the Social Democratic Party merged, the party today debates a new strategy document, No Glass Ceilings, in which it is argued that there need be no limit to the party's aspirations.
Certainly, Mr Ashdown sees no reason why the Liberal Democrats should not at some point form a government.
Meanwhile, the policy paper says that "the strategy of constructive opposition" to Labour should be maintained.
In that vein, Malcolm Bruce, the Liberal Democrats' Treasury spokesman, will tell the assembly this morning that Gordon Brown, the Chancellor of the Exchequer, should start spending some of the Government's pounds 200bn "war-chest", thus helping to deliver Labour's pledges on health, education and crime.
But an article in the conference edition of the party's magazine, The Reformer, says today that there is a danger: now that the Labour government is well on the way to delivering significant changes to the constitution, it could also satisfy demands for more investment in the public services - wiping out another Liberal Democrat demand.
In that case, the magazine says, the Liberal Democrats would need to carve out a distinctive policy stance on other issues, such as education and environment policy, welfare reform, and Europe.