Megvii, an artificial intelligence start-up, told Chinese state media that the surveillance system could give the police a search engine for crime, analyzing huge amounts of video footage to intuit patterns and warn the authorities about suspicious behavior. He explained that if cameras detected a person spending too much time at a train station, the system could flag a possible pickpocket.

Hikvision, that aims to predict protests. The system collects data on legions of Chinese petitioners, a general term in China that describes people who try to file complaints about local officials with higher authorities.

It then scores petitioners on the likelihood that they will travel to Beijing. In the future, the data will be used to train machine-learning models, according to a procurement document.

Local officials want to prevent such trips to avoid political embarrassment or exposure of wrongdoing. And the central government doesn’t want groups of disgruntled citizens gathering in the capital.

A Hikvision representative declined to comment on the system.

Under Mr. Xi, official efforts to control petitioners have grown increasingly invasive. Zekun Wang, a 32-year-old member of a group that for years sought redress over a real estate fraud, said the authorities in 2017 had intercepted fellow petitioners in Shanghai before they could even buy tickets to Beijing. He suspected that the authorities were watching their communications on the social media app WeChat.

The Hikvision system in Tianjin, which is run in cooperation with the police in nearby Beijing and Hebei Province, is more sophisticated.

The platform analyzes individuals’ likelihood to petition based on their social and family relationships, past trips and personal situations, according to the procurement document. It helps the police create a profile of each, with fields for officers to describe the temperament of the protester, including “paranoid,” “meticulous” and “short tempered.”

Many people who petition do so over government mishandling of a tragic accident or neglect in the case — all of which goes into the algorithm. “Increase a person’s early-warning risk level if they have low social status or went through a major tragedy,” reads the procurement document.

When the police in Zhouning, a rural county in Fujian Province, bought a new set of 439 cameras in 2018, they listed coordinates where each would go. Some hung above intersections and others near schools, according to a procurement document.

Nine were installed outside the homes of people with something in common: mental illness.

While some software tries to use data to uncover new threats, a more common type is based on the preconceived notions of the police. In over a hundred procurement documents reviewed by The Times, the surveillance targeted blacklists of “key persons.”

These people, according to some of the procurement documents, included those with mental illness, convicted criminals, fugitives, drug users, petitioners, suspected terrorists, political agitators and threats to social stability. Other systems targeted migrant workers, idle youths (teenagers without school or a job), ethnic minorities, foreigners and those infected with H.I.V.

The authorities decide who goes on the lists, and there is often no process to notify people when they do. Once individuals are in a database, they are rarely removed, said experts, who worried that the new technologies reinforce disparities within China, imposing surveillance on the least fortunate parts of its population.

In many cases the software goes further than simply targeting a population, allowing the authorities to set up digital tripwires that indicate a possible threat. In one Megvii presentation detailing a rival product by Yitu, the system’s interface allowed the police to devise their own early warnings.

With a simple fill-in-the-blank menu, the police can base alarms on specific parameters, including where a blacklisted person appears, when the person moves around, whether he or she meets with other blacklisted people and the frequency of certain activities. The police could set the system to send a warning each time two people with a history of drug use check into the same hotel or when four people with a history of protest enter the same park.

Yitu did not respond to emailed requests for comment.

In 2020 in the city of Nanning, the police bought software that could look for “more than three key people checking into the same or nearby hotels” and “a drug user calling a new out-of-town number frequently,” according to a bidding document. In Yangshuo, a tourist town famous for its otherworldly karst mountains, the authorities bought a system to alert them if a foreigner without a work permit spent too much time hanging around foreign-language schools or bars, an apparent effort to catch people overstaying their visas or working illegally.

In Shanghai, one party-run publication described how the authorities used software to identify those who exceeded normal water and electricity use. The system would send a “digital whistle” to the police when it found suspicious consumption patterns.

The tactic was likely designed to detect migrant workers, who often live together in close quarters to save money. In some places, the police consider them an elusive, and often impoverished, group who can bring crime into communities.

The automated alerts don’t result in the same level of police response. Often, the police give priority to warnings that point to political problems, like protests or other threats to social stability, said Suzanne E. Scoggins, a professor at Clark University who studies China’s policing.

At times, the police have stated outright the need to profile people. “Through the application of big data, we paint a picture of people and give them labels with different attributes,” Li Wei, a researcher at China’s national police university, said in a 2016 speech. “For those who receive one or more types of labels, we infer their identities and behavior, and then carry out targeted pre-emptive security measures.”

Mr. Zhang first started petitioning the government for compensation over the torture of his family during the Cultural Revolution. He has since petitioned over what he says is police targeting of his family.

As China has built out its techno-authoritarian tools, he has had to use spy movie tactics to circumvent surveillance that, he said, has become “high tech and Nazified.”

When he traveled to Beijing in January from his village in Shandong Province, he turned off his phone and paid for transportation in cash to minimize his digital footprint. He bought train tickets to the wrong destination to foil police tracking. He hired private drivers to get around checkpoints where his identification card would set off an alarm.

The system in Tianjin has a special feature for people like him who have “a certain awareness of anti-reconnaissance” and regularly change vehicles to evade detection, according to the police procurement document.

Whether or not he triggered the system, Mr. Zhang has noticed a change. Whenever he turns off his phone, he said, officers show up at his house to check that he hasn’t left on a new trip to Beijing.

Credit…Zhang Yuqiao

Even if police systems cannot accurately predict behavior, the authorities may consider them successful because of the threat, said Noam Yuchtman, an economics professor at the London School of Economics who has studied the impact of surveillance in China.

“In a context where there isn’t real political accountability,” having a surveillance system that frequently sends police officers “can work pretty well” at discouraging unrest, he said.

Once the metrics are set and the warnings are triggered, police officers have little flexibility, centralizing control. They are evaluated for their responsiveness to automated alarms and effectiveness at preventing protests, according to experts and public police reports.

The technology has encoded power imbalances. Some bidding documents refer to a “red list” of people whom the surveillance system must ignore.

One national procurement document said the function was for “people who need privacy protection or V.I.P. protection.” Another, from Guangdong Province, got more specific, stipulating that the red list was for government officials.

Mr. Zhang expressed frustration at the ways technology had cut off those in political power from regular people.

“The authorities do not seriously solve problems but do whatever it takes to silence the people who raise the problems,” he said. “This is a big step backward for society.”

Mr. Zhang said that he still believed in the power of technology to do good, but that in the wrong hands it could be a “scourge and a shackle.”

“In the past if you left your home and took to the countryside, all roads led to Beijing,” he said. “Now, the entire country is a net.”

Isabelle Qian and Aaron Krolik contributed research and reporting. Production by Agnes Chang and Alexander Cardia.

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Elon Musk Races to Secure Financing for Twitter Bid

Elon Musk is racing to secure funding for his $43 billion bid to buy Twitter.

Morgan Stanley, the investment bank working with Mr. Musk on the potential deal, has been calling banks and other potential investors to shore up financing for the offer, four people with knowledge of the situation said. Mr. Musk is first focused on raising debt and has not yet begun to seek equity financing for his bid, one of the people said.

Mr. Musk is evaluating various packages of debt, including more senior debt known as preferred debt and a loan against his shares of Tesla, the electric carmaker that he runs, two of the people said. Apollo Global Management, the private equity firm, is among the parties considering offering debt financing in a bid for Twitter. The equity he needs is likely to be sizable.

Mr. Musk is aiming to pull together a fully funded offer as soon as this week, one of the people said, though that timeline is far from certain. The people with knowledge of the discussions were not authorized to speak publicly because the details are confidential and in flux.

It is unclear if Mr. Musk’s efforts will be successful, but they go toward addressing a key question about his Twitter bid. Last week, Mr. Musk, the world’s wealthiest man, made an unsolicited offer for the social media company, saying that he wanted to take it private and that he wanted people to be able to speak more freely on the service. But his offer was regarded skeptically by Wall Street because he did not include details about how he would come up with the money for the deal.

poison pill.” A poison pill would effectively prevent Mr. Musk from owning more than 15 percent of Twitter’s shares. The 50-year-old had been building up a stake in the company and owns more than 9 percent of Twitter, making him at one point its single-biggest individual shareholder.

Mr. Musk, whose net worth has been reported at $255 billion, did not respond to a request for comment. On Tuesday, in what appeared to be a veiled allusion to Twitter, he tweeted his thoughts about social networks and their policies.

funding secured,” propelling Tesla shares higher. He did not have financing prepared for such a deal. The Securities and Exchange Commission later filed a securities fraud lawsuit against him, accusing him of misleading investors. Mr. Musk paid a $20 million fine and agreed to step aside as Tesla’s chairman for three years.

Some investors are wary of getting involved in financing Mr. Musk’s Twitter bid, concerned about the risks of teaming up with the mercurial billionaire and a company as politically contentious as Twitter, one person with knowledge of the situation said. For banks, offering a loan against Tesla stock is also risky, given the stock’s volatility.

Mr. Musk has not publicly articulated his business plan for Twitter, though he has spoken about reversing Twitter’s moderation policies and providing additional transparency about how its algorithms work. He has made clear that profit is not his focus, potentially complicating efforts to invest with traditional Wall Street financiers.

“This is not a way to sort of make money,” Mr. Musk said in an interview at a TED conference last week. “My strong intuitive sense is that having a public platform that is maximally trusted and broadly inclusive is extremely important.”

Mr. Musk’s offer for Twitter stands at $54.20 a share. Several analysts have said the company’s board is likely to accept only an offer of $60 a share or more. Twitter’s stock rose above $70 a share last year when the company announced goals to double its revenue, though its stock has since fallen to around $45 as investors have questioned its ability to meet those targets.

join the company’s board. At the time, Parag Agrawal, Twitter’s chief executive, and other board members said they welcomed Mr. Musk as a director given his use of the platform. Mr. Musk has more than 82.5 million Twitter followers and tweets frequently.

Mr. Musk and Mr. Agrawal also share similar perspectives about how to decentralize Twitter so that users can gain more control over their social media feeds, a tactic that both men see as a way of promoting more free speech. That move would also reduce the burden on Twitter, which has faced questions about toxic content and misinformation, to decide what posts can stay up and what should be taken down.

But then Mr. Musk rejected the board seat and began the effort to take over the company.

Twitter, which has brought on advisers from Goldman Sachs and JPMorgan Chase, has also been weighing whether to invite bids from other potential buyers, two people close to the company said. At least one interested party, the private equity firm Thoma Bravo, has emerged, though it is unclear whether it will ultimately submit an offer.

Kate Conger, Mike Isaac and Jack Ewing contributed reporting.

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Twitter Counters Elon Musk’s Takeover Bid With a Poison Pill

Poison pills have been around for decades. The lawyer Martin Lipton, a founding partner of Wachtell, Lipton, Rosen & Katz, invented the maneuver, also called a shareholder rights plan, in 1982. It was a way to shore up a company’s defenses against unwanted takeovers by so-called corporate raiders like Carl Icahn and T. Boone Pickens.

They have since become a part of the corporate tool kit in America. Netflix adopted a poison pill in 2012 to stop Mr. Icahn from buying up its shares. Papa John’s used one against the pizza chain’s founder and chairman, John Schnatter, in 2018.

Investors rarely try to get around a poison pill by buying shares beyond the threshold set by the company, according to securities experts. One said it would be “financially ruinous,” even for Mr. Musk.

But Mr. Musk, who is worth more than $250 billion and is the chief executive of Tesla and SpaceX, rarely abides by precedent. He announced his intention to acquire Twitter on Thursday, making public an unsolicited bid worth more than $40 billion. In an interview at a TED conference later that day, he took issue with Twitter’s moderation policies, which govern the content shared on the platform.

Twitter is the “de facto town square,” Mr. Musk said, adding that “it’s really important that people have the reality and the perception that they are able to speak freely within the bounds of the law.” Twitter currently bans many types of content, including spam, threats of violence, the sharing of private information and coordinated disinformation campaigns.

Mr. Musk argued that taking Twitter private would allow more free speech to flow on the platform. “My strong intuitive sense is that having a public platform that is maximally trusted and broadly inclusive is extremely important to the future of civilization,” he said during the TED interview. He also insisted that the algorithm Twitter uses to rank its content, deciding what hundreds of millions of users see on the service every day, should be public for users to audit.

Mr. Musk’s concerns are shared by many executives at Twitter, who have also pressed for more transparency about its algorithms. The company has published internal research about bias in its algorithms and funded an effort to create an open, transparent standard for social media services.

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Twitter Wants to Reinvent Itself, by Merging the Old With the New

The Bluesky project would eventually allow for the creation of new curation algorithms, which would show different tweets at the top of users’ timelines than Twitter’s own algorithm. It would give users more choice about the kinds of content they saw, Mr. Dorsey said, and could allow Twitter to interoperate with other social media services.

Bluesky grabbed the attention of many technologists who were already working on decentralization. Soon small groups of them were meeting with Mr. Agrawal and Mr. Dorsey on Sundays to discuss the project, according to two participants who spoke on the condition of anonymity to discuss the private meetings, while others traded ideas in an online chat room.

Some Bluesky participants proposed a single app that piped in all their social media feeds. Others wanted custom algorithms that could, for instance, block them from seeing spoilers about their favorite TV show. And some were focused on making their online identities portable, so that an account could be moved between social media companies the way a phone number can be moved from AT&T to Verizon.

“One of the things that Bluesky would offer is curation and filtering experiences that are independent of those offered by the social media proprietorships,” said Tim Bray, an internet software pioneer and a former vice president at Amazon who participated in some of the discussions.

Jay Graber, a cryptocurrency developer, was selected in August to lead the Bluesky organization. And in February, Ms. Graber announced that the project had officially registered as a public benefit corporation and was building a prototype.

The project caught the attention of engineers at Reddit, who had preliminary discussions with Twitter engineers about how their sites might someday interoperate, two people familiar with the conversations said, but the companies have not formally agreed to any plans to work together.

Some skeptics believe Twitter is jumping on the web3 bandwagon, joining a trendy movement in tech to shift many services, including social media, to so-called blockchain technology. But executives say that Twitter is catering to what an overwhelming number of users want, while following the decentralization mandate laid out by Mr. Dorsey before he departed as C.E.O. in November.

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Who Is the Real China? Eileen Gu or the Chained Woman?

Two women have dominated Chinese social media during the Beijing Winter Olympics.

One is Eileen Gu, the 18-year-old skier born and raised in California who won a gold medal for China. The other is a mother of eight who was found chained around her neck to the wall of a doorless shack.

The Chinese internet is exploding with discussions about which of the two represents the real China. Many people are angry that the government-controlled algorithms glorify Ms. Gu, who fits into the narrative of the powerful and prosperous China, while censoring the chained woman, whose deplorable conditions defy that narrative.

The two women’s starkly different circumstances — celebrated vs. silenced — reflect the reality that to the Chinese state, everyone is a tool that serves a purpose until it does not.

Whether she wants it, Ms. Gu has become a powerful propaganda tool for Beijing to demonstrate its appeal to global talent and the benefits of being loyal to China. She represents the successful China that Beijing would like the world to admire.

inconvenient truth.

“Does Eileen Gu’s success have anything to do with ordinary Chinese?” goes the headline of one viral article that was censored later.

“Can we remember these women while cheering for Eileen Gu?” asks another headline.

“To judge whether a society is civilized or not, we should not look at how successful the privileged are but how miserable the disadvantaged are,” the article said. “Ten thousand sports champions can’t wash away the humiliation of one enslaved woman, not to mention tens of thousands of them.”

The Chinese government doesn’t like where the debate is heading. The juxtaposition of the two women highlights that underneath the glamorous surface of one of the world’s largest economies lie jarring poverty and widespread abuse of women’s rights.

It defeats the purpose of recruiting star athletes like Ms. Gu: to showcase a powerful China with global appeal.

little pinks, posted a quote from a famous Chinese novel: “I love the country. But does the country love me?”

The story of the chained woman — whose name, according to the government, is Xiaohuamei (little flower plum) — has captivated the Chinese internet since a short video went viral in late January. In it, a middle-age woman with a dazed expression stood in the dark shack with a chain on her neck. Subsequent videos revealed that she had lost most of her teeth and seemed to be mentally disturbed.

conflicting statements in the following two weeks. In the latest statement on Thursday, the authorities reported that Xiaohuamei could be a victim of human trafficking and that her husband was under investigation for false imprisonment. The government had denied both earlier.

Chinese princess.” Ms. Peng accused a retired top Chinese leader of sexual assault in November, and her name remains strictly censored on the Chinese internet.

Because she avoids sensitive issues, Ms. Gu is hailed as the model athlete for the others of Chinese heritage to learn from. She’s also cited as evidence of the superiority of China’s governance model over that of the United States.

“It’s so great that the beautiful, talented Eileen Gu came back to compete for China and won,” wrote Hu Xijin, a former editor in chief of The Global Times who still writes for the Communist Party tabloid, “while the blind, disabled Chen Guangcheng went to the United States to ‘seek brightness.’” Mr. Chen is the blind human rights lawyer who was put under house arrests for years before moving to the United States in 2012.

Mr. Hu wrote that China welcomed more scientists, athletes and businesspeople. “Let China be the place to get things done,” he wrote.

Some social media users criticized Mr. Hu’s post, saying it revealed how the system thought of the disabled and the disadvantaged like Xiaohuamei.

“This is life in China,” the writer Murong Xuecun posted on Twitter. “On one side is a Winter Olympic champion who cannot be criticized. On the other side is the chained woman who is being censored. One has a bright future. The other has come to a dead end.”

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Inflation Hits the Fast Food Counter

On a chilly Tuesday afternoon this month, James Marsh stopped by a Chipotle near his suburban Chicago home to grab something to eat.

It had been a while since Mr. Marsh had been to Chipotle — he estimated he goes five times a year — and he stopped cold when he saw the prices.

“I had been getting my usual, a steak burrito, which had been maybe in the mid-$8 range,” said Mr. Marsh, who trades stock options at his home in Hinsdale, Ill. “Now it was more than $9.”

He walked out.

“I figured I’d find something at home,” he said.

The pandemic has led to price spikes in everything from pizza slices in Manhattan to sides of beef in Colorado. And it has led to more expensive items on the menus at fast-food chains, traditionally establishments where people are used to grabbing a quick bite that doesn’t hurt their wallet.

government data. And, in some cases, portions have shrunk.

“In recent years, most fast-food restaurants had, maybe, raised prices in the low single digits each year,” said Matthew Goodman, an analyst at M Science, an alternative data research and analytics firm. “What we’ve seen over the last six-plus months are restaurants being aggressive in pushing through prices.”

This comes at a time when the hypercompetitive fast-food market is booming.

Chains like McDonald’s, Chipotle and Wingstop were big winners of the pandemic as consumers, stuck at home working and tired of cooking multiple meals for their families, increasingly turned to them for convenient solutions. But in the past year, as the cost of ingredients rose and the average hourly wage increased 16 percent to $16.10 in November from a year earlier, according to government data, restaurants began to quietly bump up prices.

But making customers pay more for a burger or a burrito is a tricky art. For many restaurants, it involves complex algorithms and test markets. They need to walk a fine line between raising prices enough to cover expenses while not scaring away customers. Moreover, there isn’t a one-size-fits-all approach. Chains that are operated by franchisees typically allow individual owners to decide pricing. And national chains, like Chipotle and Shake Shack, charge different prices in various parts of the country.

When Carrols Restaurant Group, which operates more than 1,000 Burger Kings, raised prices in the second half of last year, the number of customers actually improved from the third to the fourth quarter. “Over time, we generally have not seen a whole lot of pushback from consumers” on the higher prices, Carrols’ chief executive, Daniel T. Accordino, told analysts at a conference in early January.

Menu prices are likely to continue to climb this year. Many restaurants say they are still paying higher wages to attract employees and expect food prices to rise.

“We expect unprecedented increases in our food basket costs versus 2021,” Ritch Allison, the chief executive of Domino’s Pizza, told Wall Street analysts at a conference this month. While Domino’s hasn’t raised prices, it is altering its promotions — offering the $7.99 pizza deal only to customers ordering online and shrinking the number of chicken wings in certain promotions to eight from 10 — in an effort to maintain profit margins.

Despite the higher food and labor costs, some restaurants are seeing sales and profits rebound past prepandemic levels.

When McDonald’s reports earnings this month, Wall Street analysts expect that its revenues will have hit a five-year high of more than $23 billion, a $2 billion increase from 2019. Net income is predicted to top $7 billion, up from $6 billion in 2019. Other chains like Cracker Barrel and Darden Restaurants, which owns Olive Garden and Longhorn Steakhouse, have resumed dividend payments or cash buybacks of stock after suspending those activities early in the pandemic to conserve cash.

And next month, when Chipotle reports results for 2021, analysts expect revenues to top $7.5 billion, a 34 percent jump from 2019. Net income is expected to almost double from prepandemic levels. In the third quarter, the company repurchased nearly $100 million of its stock. Chipotle declined to make an executive available for an interview, citing the quiet period ahead of its earnings release.

While Chipotle executives blamed higher labor costs for a 4 percent price increase in menu items this summer, the company has been looking for ways to boost its profitability.

One way was to charge higher prices for delivery. Delivery orders through vendors like DoorDash and Uber Eats exploded for Chipotle and other fast-food chains during the pandemic. But so did the commission fees that Chipotle paid the vendors. So in the fall of 2020, it began running tests to see what would happen if it raised the prices of burritos and guacamole and chips that customers ordered for delivery, executives told Wall Street analysts in an earnings call. It essentially meant the customer covered Chipotle’s side of the delivery costs.

The company discovered customers were willing to pay for the convenience of delivery. Now, customers ordering Chipotle for delivery pay about 21 percent more than if they had ordered and picked the food up in the stores, according to an analysis by Jeff Farmer, an analyst at Gordon Haskett Research Advisors.

“I would say that our ultimate goal, so this would be over the long term, maybe the medium term, is to fully protect our margins,” said Jack Hartung, the chief financial officer of Chipotle, on a call with Wall Street analysts last fall. “When you look at our pricing versus other restaurant companies’ for the quality of the food, the quantity of the food, and the quality and convenience of the experience, we offer great value. So we believe we have room to fully protect the margin.”

That doesn’t mean customers are thrilled about the extra costs.

This month, Jacob Herlin, a data scientist in Lakewood, Colo., placed an order: a steak-and-guacamole burrito for $11.95, a Coca-Cola for $3, and chips and guacamole, which were free with a birthday coupon. The total was $14.95, before tax.

But when he clicked to have the food delivered, the price for the burrito jumped to $14.45 and the soda climbed to $3.65, bringing the total to $18.10 before tax, 21 percent more than if he had picked the food up himself.

There was more. Mr. Herlin was charged a delivery fee of $1 and another “service fee” of $2.32, bringing the total for the delivered meal to $23.20. He tipped the driver an additional $3.

Mr. Herlin said he did not mind paying for delivery and wanted drivers to be paid a decent wage. But he felt that Chipotle wasn’t being upfront with customers about the added costs.

“They’re basically hiding the fees two different ways, through that base price increase and through the hidden ‘service fee,’” Mr. Herlin said in an email. “I would very much prefer if they had the same pricing and were just honest about a $5 delivery fee.”

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In India, Facebook Struggles to Combat Misinformation and Hate Speech

On Feb. 4, 2019, a Facebook researcher created a new user account to see what it was like to experience the social media site as a person living in Kerala, India.

For the next three weeks, the account operated by a simple rule: Follow all the recommendations generated by Facebook’s algorithms to join groups, watch videos and explore new pages on the site.

The result was an inundation of hate speech, misinformation and celebrations of violence, which were documented in an internal Facebook report published later that month.

bots and fake accounts tied to the country’s ruling party and opposition figures were wreaking havoc on national elections. They also detail how a plan championed by Mark Zuckerberg, Facebook’s chief executive, to focus on “meaningful social interactions,” or exchanges between friends and family, was leading to more misinformation in India, particularly during the pandemic.

a violent coup in the country. Facebook said that after the coup, it implemented a special policy to remove praise and support of violence in the country, and later banned the Myanmar military from Facebook and Instagram.

In Sri Lanka, people were able to automatically add hundreds of thousands of users to Facebook groups, exposing them to violence-inducing and hateful content. In Ethiopia, a nationalist youth militia group successfully coordinated calls for violence on Facebook and posted other inflammatory content.

Facebook has invested significantly in technology to find hate speech in various languages, including Hindi and Bengali, two of the most widely used languages, Mr. Stone said. He added that Facebook reduced the amount of hate speech that people see globally by half this year.

suicide bombing in the disputed border region of Kashmir set off a round of violence and a spike in accusations, misinformation and conspiracies between Indian and Pakistani nationals.

After the attack, anti-Pakistan content began to circulate in the Facebook-recommended groups that the researcher had joined. Many of the groups, she noted, had tens of thousands of users. A different report by Facebook, published in December 2019, found Indian Facebook users tended to join large groups, with the country’s median group size at 140,000 members.

Graphic posts, including a meme showing the beheading of a Pakistani national and dead bodies wrapped in white sheets on the ground, circulated in the groups she joined.

After the researcher shared her case study with co-workers, her colleagues commented on the posted report that they were concerned about misinformation about the upcoming elections in India.

Two months later, after India’s national elections had begun, Facebook put in place a series of steps to stem the flow of misinformation and hate speech in the country, according to an internal document called Indian Election Case Study.

The case study painted an optimistic picture of Facebook’s efforts, including adding more fact-checking partners — the third-party network of outlets with which Facebook works to outsource fact-checking — and increasing the amount of misinformation it removed. It also noted how Facebook had created a “political white list to limit P.R. risk,” essentially a list of politicians who received a special exemption from fact-checking.

The study did not note the immense problem the company faced with bots in India, nor issues like voter suppression. During the election, Facebook saw a spike in bots — or fake accounts — linked to various political groups, as well as efforts to spread misinformation that could have affected people’s understanding of the voting process.

In a separate report produced after the elections, Facebook found that over 40 percent of top views, or impressions, in the Indian state of West Bengal were “fake/inauthentic.” One inauthentic account had amassed more than 30 million impressions.

A report published in March 2021 showed that many of the problems cited during the 2019 elections persisted.

In the internal document, called Adversarial Harmful Networks: India Case Study, Facebook researchers wrote that there were groups and pages “replete with inflammatory and misleading anti-Muslim content” on Facebook.

The report said there were a number of dehumanizing posts comparing Muslims to “pigs” and “dogs,” and misinformation claiming that the Quran, the holy book of Islam, calls for men to rape their female family members.

Much of the material circulated around Facebook groups promoting Rashtriya Swayamsevak Sangh, an Indian right-wing and nationalist group with close ties to India’s ruling Bharatiya Janata Party, or B.J.P. The groups took issue with an expanding Muslim minority population in West Bengal and near the Pakistani border, and published posts on Facebook calling for the ouster of Muslim populations from India and promoting a Muslim population control law.

Facebook knew that such harmful posts proliferated on its platform, the report indicated, and it needed to improve its “classifiers,” which are automated systems that can detect and remove posts containing violent and inciting language. Facebook also hesitated to designate R.S.S. as a dangerous organization because of “political sensitivities” that could affect the social network’s operation in the country.

Of India’s 22 officially recognized languages, Facebook said it has trained its A.I. systems on five. (It said it had human reviewers for some others.) But in Hindi and Bengali, it still did not have enough data to adequately police the content, and much of the content targeting Muslims “is never flagged or actioned,” the Facebook report said.

Five months ago, Facebook was still struggling to efficiently remove hate speech against Muslims. Another company report detailed efforts by Bajrang Dal, an extremist group linked with the B.J.P., to publish posts containing anti-Muslim narratives on the platform.

Facebook is considering designating the group as a dangerous organization because it is “inciting religious violence” on the platform, the document showed. But it has not yet done so.

“Join the group and help to run the group; increase the number of members of the group, friends,” said one post seeking recruits on Facebook to spread Bajrang Dal’s messages. “Fight for truth and justice until the unjust are destroyed.”

Ryan Mac, Cecilia Kang and Mike Isaac contributed reporting.

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Racial Bias Skewed Small-Business Relief Lending, Study Says

But Sergey Chernenko, an associate professor of finance at Purdue University’s Krannert School of Management, who was not involved in Dr. Howell’s research, said the new paper aligned with his own findings on race-based gaps in Paycheck Protection Program lending. At an economic conference next month, he will present a paper that concluded that Black-owned businesses were disproportionately left out of the relief program.

“This fits very well with and complements our finding that minority-owned businesses were less likely to get loans because of racial bias, and to the extent that they do get them, they’re more likely to get them from fintechs than banks,” Dr. Chernenko said.

The government designed the Paycheck Protection Program to be virtually risk-free for lenders: They would advance small companies up to $10 million — the size of the loan was based on the company’s head count and payroll — and the government would then pay off the loans in full for business owners that followed the rules. If the borrower defaulted, the government would still repay the lender. In theory, any lender should have been willing to lend to any qualified applicant.

It didn’t work out that way. Many banks limited their loans to their current customers, which was a hurdle for owners who lacked business checking accounts or loans. But even Black owners who had accounts were noticeably more likely than those of other races to end up with a fintech loan, Dr. Howell and her co-authors found.

The effects were strongest in parts of the country with higher levels of racial animus, which the study measured with variables like the extent of local housing segregation and the prevalence of racially charged Google searches.

The researchers tested — and found little evidence for — other common hypotheses about the program’s racial lending disparities. Even after controlling for variables like the applicant’s ZIP code, industry, recent revenue, affinity for online lenders, and loan size and approval date, the gap persisted.

This was not the case, they found, at the nation’s biggest banks. After researchers controlled for those elements, Black-owned businesses appeared to be just as likely as any other to get a loan from Bank of America, Citibank, JPMorgan Chase and Wells Fargo.

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