I notice that in New Zealand, yes the same place where very fair MMP is in place, the touchstone of our world-wide movement, it is said that receiving a majority of votes is reason for the election of a candidate when nothing of the sort is meant.
The official results announces that successful candidates won with so much "majority" when what is meant is lead over nearest competitor.
Such as in the Northland electorate. Willow-Jean Prime is said to have been elected by a majority of 163 but actually only got 38 percent of the vote.
Her lead over her nearest contender was 163, but she needed 5000 more votes than she received if she was to get a majority of the valid votes.
See
https://elections.nz/media-and-news/2020/2020-general-election-official-results/
In its defence, If there are only two candidates, the majority vote taken by the winning candidate may be almost the same as the lead of one candidate over the other. Certainly the winning candidate will take a majority of the votes. But where there are more than two candidates, such as in Christchurch electorates or in Invercargill, the winner may not take a majority of the votes at all. Under FPTP, it is common for a candidate to be elected despite not getting a majority of the votes at all.
In Invercargill, for another example, the official results gives the winner's majority as 224, but she actually did not have a majority at all - Penny Simmonds received less than 45 percent of the vote. It seems that this happened in many districts, just as it happens all too often in all FPTP elections. But usually elsewhere, unlike in NZ, there are no supplemental members to offset the distortions. 37 of the district winners apparently won with less than a majority of the vote in the district. (source: online - Spinoff "A better visual breakdown of the 2020 election results")
Although in each case, each is said to have won with majority of so many hundreds or thousands of votes, such was not in fact the case.
Mistaken beliefs such as this are what allows non-proportional FPTP to have the support that it has today -- as well as basic inertia. When in fact it is deeply flawed and produces un-prorotoional governments constantly.
The wide variance needed to be elected in systems that do not use quota
A big difference between proportional systems and non-proportional that may be worth stressing is the wide variance needed to be elected in systems that do not use quota.
When mere plurality is needed to win, when votes are split in variety of ways from district to district, when voter turn-out varies, when size of district varies, there is little standardization, and thus little relationship between vote share or vote tallies to representation from candidate to candidate or from party to party.
Say in the last Edmonton election
conducted with 12 single-member plurality ward elections,
one Councillor was elected with less than 3500 votes; another with almost 12,000 votes. As well, there were nine people who received more than 3500 votes who were not elected. This includes one who got more than 5200 votes, half again more than the least-popular successful candidate.
(Other problems: more than a third of the time - a candidate with the support of only a minority of district voters was elected and no others were, thus leaving the majority in the district un-represented. These wasted votes sometimes exceed two-thirds of the votes cast in a district and is seldom less than a third of the votes cast. Overall, more than half the votes were disregarded.)
Alberta provincially 2019
Premier Rachel Notley, one of the most popular candidate anywhere, got 9500 votes, 65 percent of the votes cast in the district.
In a different district, UCP leader Kenny, who would replace Notley as premier, got 12,000 votes, 66 percent of the vote.
In Athabasca... the UCP candidate did even better 17,000 votes, 69 percent.
In Innisfail the UCP candidate got 19,000 votes, 75 percent.
In Olds-Didsbury the successful candidate (UCP) got 21,000 votes, 79 percent of the vote.
But meanwhile compared to these titans,
In Calgary Falconridge the successful candidate (UCP) got 6800 votes, 48 percent of the district vote.
In Calgary McCall the successful candidate (NDP) got 6600 votes, 52 percent of the vote in the district.
in 2015 Alberta provincial election
Calgary Buffalo was a slow race -- 4602 votes were enough to win,
while Calgary Glenmore's contest was a fast race -- where 7015 votes were not enough to win.
Federally
there is wide variation at the federal level under FPTP. In one riding in Saskatchewan, Desneth, only 26,000 votes were cast in 2019, while the average riding in Toronto had 50,000 votes cast. SMALL (sparsely-populated) rural ridings (but large in size)
In Desneth, SK 12,000 votes (42 p.c.) was enough to win.
Labrador (NL) (extremely rural -- 294,000 square kilometres in size) 12,000 votes cast. 4900 votes was enough to be elected (43 p.c.)
St. Laurent, Quebec (rural 42 square kilometres) 41,000 votes cast. the successful candidate got 24,000 votes (59 percent)
LARGE (urban) ridings
(miniscule in size - sometimes less than 6 square kilometres in land area)
Peterborough 70,000 votes cast. the successful candidate got 27,000 votes (39 percent) Toronto Centre (6 square kilometres) 55,000 votes cast. the successful candidate got 31,000 votes (57 percent)
Toronto St. Pauls 60,00 votes cast. the successful candidate got 32,000 votes (54 percent)
Calgary Shepard 79,000 votes cast. the successful candidate got 59,000 votes (75 percent)
(Note that these are size-sorted by urban and rural, not East or West, although the North is more rural than the South. Alberta, oddly enough, is one of the more urbanized provinces, so is actually under-represented by population across the country.)
Scientific voting
It is interesting to notice the contrast between St. Laurent and Peterborough.
the two successful candidates received about the same number of votes;
each took one seat,
but one was elected with a large majority of the district votes, the other with a minority of the district votes.
In one the majority of the district voters was represented; in the other the majority was un-represented and disregarded.
It is comparisons like this that make the need for scientific representation, as PR used to be occasionally called, so important.
In STV, by comparison, the variance is much less.
There are no variance in the size of the arbitrary districts (voters form themselves into similarly- sized constituencies to each elect its own rep)
and there is no variance in turnout, at least none is measured if the area is a single grouped district.
a single standard quota is used across the broader district, usually a city-wide district.
and that quota is used to declare most candidates elected, a couple or so possibly being elected at the end by mere survival.
in five-member STV district the quota would be 17 percent.
likely three members would have that number of votes and be declared elected. They would each have this exact number, no more and no less, any surplus being transferred away.
The last two would have something less than that, but likely more than half the quota each.
the exhausted votes make exact prediction impossible.
But these basic facts are known:
With three seats filled, half the votes have been used. 3 times 17 percent.
the remaining half of the valid votes (minus any exhausted votes) would be spread over the remaining candidates, as they steadily are eliminated and the vote transferred.
At the end this might come down to the remaining votes in play being gathered on three candidates, mostly on the two most popular of these. So at least two thirds of the remaining votes would be gathered on these two, who would be elected.
A pretty standard structure of vote tallies compared to non-proportional winner-take-all FPTP.
And note that about 80 to 90 percent of the votes (barring exhausted votes) were used effectively to elect someone.
and note that the proportion that were used to elect the representatives is likely far more than 70 percent of the vote (exhausted votes seldom exceeding 20 percent of the votes),
and note that the proportion used to elect the representatives is never less than a majority.
This is a far cry from the result possible under non-proportional FPTP where often as much as 65 percent of the votes are ignored.
Regionalism
Under non-proportoinal FPTP, often a city give its seats to candidates of just one party --- say Calgary to Conservatives and Edmonton to NDP --- while the large minority of supporters of the other party in each city has little or none representation.
And to think that Edmonton Conservatives can count on sympathetic treatment by Calgary MLAs or that Calgary NDP-ers can count on sympathetic treatment by Edmonton MLAs is putting a lot of trust in that party (or class) connection.
or Montreal with its Liberal reps, Toronto with its NDP reps (in the old days I would have said Conservative), etc.or federally when Alberta elected 33 Conservatives (all but one of its MPs), while BC elected 17 Conservatives (out of its 42 MPs), or Quebec elected only 10 Conservatives (out of 78 of the province's MPs).
District non-proportionality breeds regionalism
FPTP is non-proportional at the district level. Through natural process (weakness begetting weakness and strength begetting strength; disregarded voters staying home, happy voters participating in greater number) and to un-natural processes (such as gerrymandering and party allocation of resources), FPTP produces regional disparities.
Multi-member districts (such as under STV) produce mixed representation in each district (that is, in each city and in each province and in each region). And it thus prevents regional disparity --- naturally, organically and synergistically.
Thanks for reading.
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